Memory Alpha
Memory Alpha

List of unnamed Federation starships of the Constitution-class.

Docked at Starbase 1

Docked at Starbase 1

This ship was docked at Starbase 1 at the same time the USS Enterprise was undergoing repairs following their encounter with the Gorn. (SNW: "Spock Amok")

Docked at Starbase 28

Starbase 28 with two docked ships

A display graphic of Starbase 28 showed two Constitution-class starships present. (ST: "Ask Not")

One of these was presumably the visiting USS Enterprise.

Docked at Spacedock

These two vessels were in Earth Spacedock following the Whale Probe incident in 2286. The travel pod transporting the crew of the USS Enterprise passed these vessels en route to their new assignment, the USS Enterprise-A. (Star Trek IV: The Voyage Home)

Dialogue from a deleted scene found in the shooting script (scene 27) for the two dock controllers stated, "Excelsior and Intrepid are cleared to depart. Open spacedock doors", followed by the failure of both ships to power up and the doors to open, due to influence by the Whale Probe.
Two spacedock control LCARS graphics, ultimately not used in the film, confirmed the presence of the two Constitution-class vessels, as they clearly showed two berthed class vessels of which one was labeled with the registry NCC-1707, abbreviated to "NCC-177" on one of the graphics. As the graphics showed NCC-1707's departure vector alongside that of Excelsior's, has made NCC-1707 a very good candidate for Intrepid as it corresponded with the dialog in the deleted scene. The NCC-1707 registry originated from FASA's Federation Ship Recognition Manual (second edition, p. 11), at that point in time still considered an official reference work, where this Intrepid was listed as the refit-configuration replacement of USS Intrepid (NCC-1631), lost in the Star Trek: The Original Series-era, mentioned as such in Diane Duane's novel My Enemy, My Ally.
The two graphics were separately sold as Lot 1779 and Lot 6984 in two It's A Wrap! sale and auctions in 2007 and 2008 respectively. The featured shots of the two nacelles were obviously taken off the refit-Enterprise studio model.

Fleet Museum ship

This pre-refit starship was on exhibit at the Fleet Museum during the late-24th century.

Jean-Luc Picard, who identified the holographic bridge of the USS Enterprise as belonging to the Constitution-class, recognized the design from his familiarity with the one on display at the museum. (TNG: "Relics")

This starship was only mentioned in dialogue.
See also: USS Republic.

Wolf 359

At least one vessel participated in the Battle of Wolf 359 in 2366. Wreckage of the vessel or vessels was seen there as the USS Enterprise-D passed through the "grave yard" of ships that were defeated in the battle. (TNG: "The Best of Both Worlds, Part II")

The ship (or ships) in question can be seen in two different FX shots. The first is a glimpse of a badly-damaged saucer section, and the second is a that of the secondary hull. The two parts appear in different portions of the scene, which would indicate either two different vessels, or one ship that was cut apart by the Borg or that performed a saucer separation maneuver.
Behind the scenes sources indicate the model used for both shots was that of the self-destructed Enterprise made for Star Trek III: The Search for Spock. (Special Edition DVD text commentary) See also: Battle-damaged refit model.
The cover of issue 7 in the Doctor Who crossover miniseries, Star Trek: The Next Generation - Doctor Who: Assimilation², features the engineering hull wreck and a second intact Constitution-class ship getting hit by the Borg Cube, suggesting there were in fact two ships.