Near-warp transport, also known as touch-and-go downwarping, is a process whereby a starship breifly drops out of warp speed in order to use the transporter, and then quickly returns to warp as the object or person being transported is still materializing. To execute this procedure required precise timing and precision.
This procedure was used by the crew of the USS Enterprise-D in 2365 when transporting an away team down to Gravesworld to respond to a distress call from that planet. Due to a concurrent medical emergency on the USS Constantinople, Commander Riker suggested using near-warp transport in order to minimize the amount of time it would take the Enterprise to reach the Constantinople. After materialization was complete, Counselor Troi noted that, for a moment, she had felt as though she had been stuck in a nearby wall, and Lieutenant Worf informed her that is indeed what happened to her, a side effect of the near-warp transport. (TNG: "The Schizoid Man")