This page contains information regarding Star Trek: Strange New Worlds, and thus may contain spoilers.
In 2268, the Excalibur was assigned to a fleet war games exercise pitting four starships against the USS Enterprise, which was controlled by the revolutionary (but still experimental) M-5 multitronic unit. However, when the M-5 malfunctioned, it caused the Enterprise to fire phasers on the Excalibur at full power, when the ship's deflector shields were at minimum intensity. The Excalibur was severely damaged, with all hands lost. (TOS: "The Ultimate Computer")
While the death of its entire crew is established, the status of the Excalibur itself is somewhat unclear. The Star Trek Chronology (2nd ed., p. 88) stated that the ship was destroyed. The fourth edition of the Star Trek Encyclopedia offerd two possible conditions of the Excalibur - the ship was severly damaged (vol. 1, p. 254) or accidentally destroyed (vol. 2, p. 329). The episode itself provided no firm confirmation either way.
The registry of the Excalibur was not confirmed until it was seen on the CGI model in the 2008 remastered version of "The Ultimate Computer". The registry was first connected with the starship in Greg Jein's influential "The Case of Jonathan Doe Starship" article, published in the April 1973 issue 27 of the T-Negative fanzine. In the article, Jein had made an attempt to "logically" couple the registry numbers as seen in "Court Martial" with the names listed in the reference book The Making of Star Trek. His conjectural ship's registry has been subsequently propagated in the Star Trek Concordance and the Star Trek Encyclopedia, the latter co-authored by future remastering project Visual Effects Producer Michael Okuda, who made use of the remastering opportunity to elevate Jein's until then conjectural ship's registry to canon. With the high definition version of "Court Martial", the registry, which had been read as NCC-1664, was determined to be NCC-1864. This registry was that of the USS Reliant.
The name of the ship had already been established by the producers at the start of second season of Star Trek: The Original Series, when they composed a list of fourteen ships belonging to the Constitution-class, still referred to as "Starship-class" by them at the time, including the Excalibur. The Excalibur has been a consideration from the start. (The Making of Star Trek, pp. 164-165) The name was considered due to the fact that page 27 of the first draft treatment of the script, dated May 15, 1967 for the second season episode "Amok Time", contained a line in which Captain Kirk stated,
The reference though, was dropped from the episode as aired. 
According to the Star Fleet Technical Manual the registry of the Excalibur was NCC-1705.