A viridium patch was a small device which could be attached to clothing and used for tracking purposes. The patch could be detected up to two sectors away.
In 2293, Captain Spock placed a viridium patch on the uniform of Captain James T. Kirk as the latter prepared to beam over to Kronos One from the USS Enterprise-A following the assassination of Klingon chancellor Gorkon. After Kirk's arrest and trial, Spock was able to use the patch to rescue Kirk and Leonard McCoy from the gulag at Rura Penthe. (Star Trek VI: The Undiscovered Country)