(written from a Production point of view)
Several studio models of the Template:ShipClass were designed and used on Star Trek: Voyager and one episode of Star Trek: Deep Space Nine. Starting out as a traditional physical studio model, advances in visual effects techniques, caused that model to be replaced with a digital counterpart halfway through the production of Voyager.
The earliest concepts for Star Trek: Voyager came in September 1993, during the last season of The Next Generation and the second season of Deep Space Nine. Star Trek producers had already begun to plan for a new series set on a smaller starship than the Enterprise-D, but instead of waiting for more clarification, Rick Sternbach immediately started making sketches of this unnamed vessel.
Sternbach's early sketches had Voyager as a streamlined, dart-like primary hull, with a flattened, elongated engineering hull, sporting swept-back runabout-like warp pylons. Later on, it was decided that Voyager would be able to land on a planetary surface, requiring deployable landing gear and other arrangements of resting-on-hull components to be sketched out. Variations filled more paper as the proportions of different parts changed, pieces were added and subtracted, and hull contours, both gently curved and angular, were explored in perspective. Even in the rough sketches, a lot of design ideas got worked out, concerning placement of familiar items like impulse engines and phasers. Not surprisingly, this exercise would be repeated in greater detail with each new approved version of the hull. Preliminary hull cross-sections were drawn in blue pencil to check different internal deck heights, total number of decks, and possibly overall ship length.
During April and May of 1994, the first real sense of the new starship emerged. The slightly angular dart front was smoothed off and nestled into the engineering sections, still assuming a separation capability, and sweeping pylons ended in a set of long nacelles. Doors on the nacelles could open, exposing the warp coils for some new kind of energy jump. Impulse thrusters were buried underneath, as in the runabout, and a large triangular wedge sat atop the ship, possibly acting as a scout craft or long-range sensor array. In this design, all of the familiar Starfleet parts were added, in type and location, much the way they eventually were. A few cut-and-paste variations were assembled, along with a sleeker version that left out the long-range sensor pod and combined a few shape ideas from the runabout and the Template:ShipClass. Here, a few more details crept in, notably the large forward sensor cut-out, and a stepped engineering hull that supported a ring of large cargo bays and impulse engines. This particular variant received additional approval from the producers and proceeded to the initial blueprint and study model stages. Sternbach scaled up a top plan view sketch of the ship to a length of 48 inches – the presumed size of the motion control model at the time. From the top view, Sternbach derived bottom, side, fore, and aft views. The side elevation (and resulting cross-section) showed 14 decks, and that the ship was about a thousand feet long (the same size as the upgraded Enterprise from The Motion Picture). This would make it about 303 meters.
There seemed to be no insurmountable problems from the design standpoint in giving it all the proper fictional starship systems, or of building and filming the miniature. The set designs could be matched in shape and color. This version of Voyager looked fast, with a hint of solid engine hardware showing on the outside. Just as Sternbach was about to produce a final set of model-maker's blueprints, the producers asked if he could make Voyager a bit more blended, more curvy; just as a physical model of the USS Voyager had been completed, the producers called for softening the hull contours. Sternbach also still worked on the nacelle placement, mounting them on pylons like on the Enterprise-D, or down-turned like on a runabout, and horizontal pylons that evolved into wings.
Following the Starfleet standard, Sternbach reserved spaces for the bridge on Deck 1 and a variety of place-holder windows on the hull, which would be built into standing sets. Windows are an important design factor because of the coordination necessary between various studio departments and an outside model-maker over continuity of the exterior of the ship and the interior. Since Voyager would be smaller, structures like windows would be proportionately larger and more visible, requiring more model details matching the stage sets. The large windows that appear on the upper side of the Voyager model were designed by Rick Sternbach to accommodate the living quarters of the starship's senior officers, the five windows located underneath the officers' mess on the fore-side of the ship being allocated to the captain's quarters. For all quarters, the same set was used on the show with removable wall segments being used to make it either a two-, three-, or four-window quarter (presumably the fifth window of the captain's quarters serviced its bathroom).
The "Voyager Prototype Model" was a study model designed by Rick Sternbach and built by Gregory Jein out of foam core and bondo during the pre-production of Star Trek: Voyager. This was a mock-up only; it was not built as a filming miniature. Featuring many details that eventually made it into the producers' final choice for the design of the Intrepid-class USS Voyager, this prototype featured sharper, more angular shapes, and long, down-swept warp nacelles mounted on pylons designed similarly to those on the Template:ShipClass runabout. This was very similar to the kitbashed filming model that was labeled USS Elkins, leading to those two models to be sometimes confused. This design came very close of becoming the definitive one for Voyager. As Sternbach remembers, "I was ready to produce a final set of modelmakers's blueprints when a request came down from the producers – they had been perusing the study model for a while – which asked if I could please make Voyager a bit more blended, a bit curvier, like a Lexus. I looked at the latest sketch and pondered a bit. Sure, I thought. Why not." (Star Trek: The Magazine Volume 1, Issue 19, p. 25). Sternbach himself later expressed a mild preference for this design over the definitive one, "(...)only once did I ever get far enough to really flesh out (and get excited about) a design that was never used, and that was the early maquette-stage Voyager I built as a foam core and bondo study model." 
The model has been on tour once, appearing in the BOSS Film Studios' model shop expo '97 in Los Angeles. No longer in the possession of either Sternbach or Paramount Pictures, the model wound up in the possession of a private collector who, until recently, was trying to sell it through eBay. 
Physical studio model
Starting on 16 June 1994, Sternbach needed about a month to re-design the model along the "curvier" lines requested before it was approved. The physical studio model, essentially a collaborative design effort by Sternbach, Richard James, and Michael Okuda (who had to match the interior sets with the outer appearance of the ship), was eventually built, after Sternbach produced detailed blueprints in August 1994, at Tony Meininger's Brazil-Fabrication & Design. Constructed out of vacuum-formed plastic and cast resin with internal neon lighting, it measured 61×24×10 inches, and was commonly referred to by the production staffers as the "five foot model".  Meininger delivered the model to Image G for shooting on 19 October 1994, though detailing continued until mid-December. (A Vision of the Future - Star Trek: Voyager, p. 217) The model was also outfitted with tiny still photographs of interior settings, positioned behind the windows. (Cinefantastique, Vol 27 #4/5, p. 46)
As the Intrepid class was capable of making landfall, the model could also be outfitted with a landing gear (also designed by Sternbach) Though the deployment of the gear was done as a CGI effect, "we had little stand-in feet we could put on that [the five-foot model] too.", effects supervisor Dan Curry said as he explained the landing sequence for the episode "The 37's" (VOY Season 2 DVD, "Red Alert: Visual Effects Season 2"-special, disc 7). It was the first and last time the model was photographed in the landing configuration as subsequent landings were entirely realized as CGI. The landing gear did not held up in close-up shots so a part of the landing gear was recreated as a larger scale physical model in May 1995.
The model enjoyed an uneventful career, but was all but replaced from VOY Season 4 onward by its digital counterpart due to the advances in the CGI technique.
The studio model made only one public appearance before being sold off at auction in 2006, when it was featured in Los Angeles at the California ScienCenter on 19 February 2004 for a release party, that also served to honor the efforts of NASA, Jet Propulsion Laboratory and others in the exploration of space, on the occasion of the first Voyager DVD release. (VOY Season 3 DVD, special features, disc 7)
The physical model, known as Lot#357 and estimated at $10,000 – $15,000 was sold on 6 October 2006 in the 40 Years of Star Trek: The Collection auction, with a winning bid of $110,000 ($132,000 including buyer's premium). The winner of the lot, Adrian Hancock from Leicester, England, was interviewed in The History Channel's documentary Star Trek: Beyond the Final Frontier. 
Other physical models
For "Parallax", effects man Joe Bauer had to construct a low budget scale model of the landing bay out of cardboard and miscellaneous kit parts since "Amblin Imaging" that was to compose the approach scene as a CGI shot, could not deliver on time and on budget. (Cinefantastique, Vol 27 #4/5, p. 83)
A commercially available model that wound up on screen was the small Christmas ornament of the USS Voyager released by Hallmark in 1996, repainted as a ship-in-a-bottle model in Joseph Carey's quarters in "Friendship One".
Another commercially available product, Revell-Monogram's model kit, No. 3604, was also slated to make an on-screen appearance, along with other models of varying starship classes, as one of the golden models in the display cases in the observation lounge of the USS Enterprise-E in Star Trek Nemesis. John Eaves built the model, filled it with resin, had it electro gold plated at ArtCraft Plating, but failed to deliver the model in time for shooting and it was subsequently never used. Eaves retained the model, "I got the other ships done in about a week and took them to the stage and he [rem : John Dwyer] had already filled the cases twice with doubles of the original 6. It was too much work to take out and replace the dups with the new so they didn't make it on the big screen, but they did wind up at my house again.", Eaves recalled.
A small scale model of Voyager was also constructed at a later stage, most likely another modified Revell-Monogram model kit, for personal use as a study model for Sternbach. It was never used for filming (nor was any other physical model used as stand-in for the studio model for that matter), and later sold on eBay.
Foam core camera test models of various sizes, one of which was featured in the "Red Alert: Visual Effects Season 2"–special on disc 7 of VOY Season 2 DVD, have been sold in the July 2008 and January 2009 It's A Wrap! sale and auctions for $305,00 , $599,00 , and $157,65  respectively.
At the time of inception of the Voyager series, however, CGI was becoming more affordable and the decision, prompted on by David Stipes was made to have also a CGI model made for the intricate title sequence in which both models were to be used. Santa Barbara Studios, the effects company responsible for creating the sequence, originally used their own low-resolution CG model while mapping out the sequence. Upon completion, their model was replaced with a more detailed and finished model built at Amblin Imaging by John Gross, Grant Bouchet and Bruce Hall, who remembered, "Wow, it been a long time since I have seen renders of that….takes me back to my Amblin days and the sweat that went into building it with David Stipes sitting over my shoulder pointing everything out that was wrong with it."  Amblin had the physical studio model scanned and digitized at Cyberscan which built a detailed CGI wire-frame model. That model was then turned over to Amblin for mapping, detailing and animation using high resolution pictures taken from the physical model. In the end their model consisted of over 300,000 polygons, one of the most complicated models of that time. (Cinefantastique, Vol. 27, No. 4/5, pp. 72-75, 79-81)
The method of mapping flat-lit photographs over a wire-frame model had a slight drawback as 2D imagery manipulated in 3D space resulted in slight distortions as Sternbach later observed, "From what I understand, the five foot filming miniature was photographed to produce the surface texture maps, the CG model was built by Santa Barbara Studios, and the projection of the maps onto the CG polygons didn't match exactly.(...)The shield grid lines and phaser strips, as well as the SIF field reinforcement strips, should be absolutely horizontal as they were in the [physical] model [rem: when seen from the side]. Tony Meininger and his Brazil Fabrication crew set up the hull perfectly straight on a flat surface and "walked" a scriber around to get the deck levels/grid lines. My guess is that the model photography introduced some kind of distortion; maybe it wasn't shot from a long enough distance away."
As a precaution and back-up, Stipes and Ronald B. Moore decided to have Santa Barbara Studios also construct a full-fledged CGI model. Using different software meant that the two models were not interchangeable. The same methodology was used as with the "Amblin" model, with their scanning and digitizing done at Viewpoint DataLabs International, Inc.. Nevertheless, it was mostly the "Amblin" model that was used in the subsequent episodes of the first two seasons of Voyager. (Cinefantastique, Vol. 27, No. 4/5, pp. 72-75, 79-81) The experience garnered by Santa Barbara Studios proved useful, however, when it came to digitizing the Enterprise-E for Star Trek: Insurrection. Still, CGI at this point was not yet perfect, as Gross explained:
"There are six shots in the opening title sequence, three of them had the CG ship that we built; the other three have the practical model. The three that had the CG ship were the one where it goes by the sun, the one where it goes through the smoky, particle stuff, and the last one, where it jumps to warp.(...)We always use beta software [rem: meant is a new version of Lightwave which at the time was available on two different computer systems}, which means there tend to be some bugs. As we were modelling Voyager, some of it was being done in the Amiga version; some was being done on the SGI version. If you transferred the model between the different systems, the textures – effectively the paint on the ship – would get lost. That happens in the final shot where the belly tips up toward us and Voyager goes to warp.
It's something you don't really pick out unless you know it's there, but if you look at the bottom of the ship there are these three darker patches that aren't supposed to be there-it's where there are some ports and hull plating. That made it into the title sequence. Nobody said anything, and we never mentioned it!" (Star Trek: The Magazine Volume 3, Issue 3, p. 112)
This made Voyager the second Star Trek series where CGI was used from its very inception to the end of its run (DS9 already had CGI elements in its title sequence and there were also the morphing effects of Odo, done as CGI). Viewers could distinguish between the CGI and physical models by observing the windows at the utmost aft under the landing bay. The CGI model had the windows lighted whereas the physical model had not since there was no room in that area of the model to install electrical wiring. As time progressed, CGI became more and more cost effective and the special effects more ambitious to a point when the physical studio model was rarely used any more in the latter seasons. After Season 2, Foundation Imaging took over the CGI work for Voyager and part of its work was remapping the "Amblin" model (and repairing the shortcomings) of Voyager, done by Robert Bonchune.  Bonchune elaborated on his work:
"As the show progressed, the need to get closer and closer to the ship meant that we were going to have to add more detail to the Voyager. This would help it to hold up to closer scrutiny by the camera. One of the things I noticed was that under certain lighting conditions the ship had a slight reddish brown hue. I went in and had a look at the maps. They were a basic neutral grey with a slight tint towards red. Now, on TV, the ship looks neutral gray, but the practical miniature is actually Duck Egg Blue. We decided to change the maps to reflect this in an effort to match the practical more closely at close range.Bonchune went on clarifying that fellow CGI artists at Foundation kept on refining the model throughout the remainder of the series as the need arose for specific episodes, especially for extreme close-ups. Adam Lebowitz, Koji Kuramura, Trevor Peirce, Doug Drexler  and Lee Stringer  all worked at one time or another on the model. A last refinement was performed after its use as production asset, by Gabriel Koerner for the "Borg Invasion 4D" ride at the Las Vegas Star Trek: The Experience attraction.
Another thing I noticed was that, when seen close, the deflector dish's light on the practical miniature faded out towards the edges. I mapped the dish to reflect this look. At his point, I just kept going. I re-mapped the bussards and the warp nacelles' warp glow area."(Sci-Fi & Fantasy Models, Issue 32, 1998, p. 54)
The versatility of the CGI model also meant that alterations beyond mere refining could be performed on the model. One of those alterations was outfitting the Voyager with ablative armor in the series finale "Endgame".