A courtroom was a room in which a court presided.
At least one courtroom was at Starbase 11. In 2267, this Starfleet courtroom was used for the court martial of Captain James T. Kirk, regarding the supposed death of Lieutenant Commander Benjamin Finney. (TOS: "Court Martial")
The Mae West film I'm No Angel featured a scene set in a courtroom. In a holographic recreation of World War II, Tom Paris, believing himself to be Bobby Davis, recalled sharing a kiss with his girlfriend, Brigitte (B'Elanna Torres), during this scene. (VOY: "The Killing Game, Part II")
- TOS: "Court Martial"
- TNG: "The Measure Of A Man"
- VOY: "The Killing Game, Part II"
Background information Edit
In the first draft script of TOS: "Court Martial" (which had the working title "Court Martial at Star Base 811"), the courtroom in that story was described as featuring a transporter. In a six-page memo of script notes Gene Roddenberry sent Gene L. Coon (on 15 August 1966), however, Roddenberry declared, "Let's lose this." On the other hand, he suggested that the courtroom contain a single master viewing screen and a computer voice.
In the final draft and revised final draft of the script for "Court Martial", the episode's courtroom was initially described thus; "The room is stark... one main viewing screen... one recorder machine (an exact copy of which we've seen earlier in Stone's office)... a witness chair above which is a circular phosphorescent light that blinks on and off as the recorder verbally capsulizes the service biography of each witness when they take the stand. In addition, wherever possible the overtone of the room should be strictly naval... highlighting this effect is the ancient naval ship's bell that Stone will ring to call the court to order." The set for this courtroom was built on Desilu Stage 10.
The Klingon courtroom in Star Trek VI was referred to simply as a courtroom in the film's script, with no direct indication of the room's placement. The script described the room as, "A cavernous stadium arranged in circular tiers cut from jagged stone. A place from a bygone age, of savage and awesome beauty. Something between a circus and a cathedral... turned for the occasion into a gigantic courtroom." The script referred to "the dock [...] in the bottom at the very center of the circle, surrounded by [...] rising tiers" and described "a darkened dugout" for Klingon judges to sit in.  A matte painting study of this Klingon courtroom was illustrated by Mark Moore from Industrial Light & Magic. (The Art of Star Trek, p. 266) The courtroom set was housed on Paramount Stage 14. (The Making of the Trek Films, UK 3rd ed., p. 114) Although it was commonly referred to in the script as a "courtroom",  the area is not referred to as such on screen. The site was also called a "courtroom" by members of the production staff. Those who were impressed with and proud of the set included Herman Zimmerman, Todd Bryant, and Leonard Nimoy. Zimmerman, a long-time Star Trek production designer, commented that the courtroom was his favorite of all the Star Trek sets he had worked on, at least until Star Trek Nemesis. Bryant noted, "When I first walked in and saw it, I was just blown away." He also likened it to a large cathedral. When Nimoy saw the set, he expressed that he'd very much like to direct some filming in the set. "[That] made me very happy," Zimmerman remarked, "because what you see on screen is not as beautiful, and it didn't need to be." ("Bringing It to Life", Star Trek VI: The Undiscovered Country (Blu-ray) special features) As evidenced by the first draft script of VOY: "Flashback", the same Klingon courtroom was originally to have briefly reappeared in that episode, represented with stock footage from Star Trek VI. In the script, the room was referred to as "the Great Klingon Hall". The idea of the courtroom reappearing was vetoed by the time the final draft of the "Flashback" teleplay was issued.
As with the Klingon courtroom, Q's courtroom was commonly referred to in the script as a "courtroom", but the area is not referred to as such on screen.   In the script of "All Good Things...", though, the room actually was referred to as a "courtroom" in dialogue, Picard stating, "The last time I stood in this courtroom was seven years ago..." and asking Q, "Why do I find myself back in this courtroom?"  Evidently, these lines were later changed, "in this courtroom" replaced by simply the word "here" in both cases. For "Encounter at Farpoint", the set for Q's courtroom was built on Paramount Stage 16. The set was constructed from pieces that were originally built for the episode's "Farpoint Mall", and were then repainted and rearranged with add-ons, grids, and drapes, to make the courtroom. (Information from Larry Nemecek) Robert Justman calculated the set as costing US$55,141.  For "All Good Things...", the set for Q's courtroom was again situated on Stage 16. (Information from call sheets)
A Cardassian courtroom in DS9: "Tribunal" was a reuse of a set usually used as Deep Space 9's holosuite. Some of the courtroom's design details were incorporated into Makbar's hairstyle. (Star Trek: Deep Space Nine Companion, p. 150)
For the usage of Deep Space 9's wardroom for a trial in DS9: "Rules of Engagement", that episode's script referred once to the wardroom as a "courtroom". The same script additionally twice referred to "courtroom dialog". 
The area used for a Klingon trial in ENT: "Judgment" was commonly referred to as "Klingon tribunal chamber" in the script of that installment. However, there was one reference to it as a "courtroom" in the script, specifically in a scene description.  Also, David A. Goodman referred to it as a "courtroom" in an audio commentary podcast about the episode.