Star Trek: Every Auxiliary Craft Explained

If you look closely at the underside of the Enterprise-D's saucer section, you can see the outline of Picard's personal Captain's Yacht, the Calypso.

Captain's Yachts were relatively large support vessels that could be used by the Captain for personal missions away from their starship. The Calypso was never used on screen, but we got to see the Enterprise-E's Captain's Yacht, The Cousteau, in action in Star Trek: Insurrection.

Captain's Yachts were basically just luxury shuttles. It's really no surprise that Picard wasn't too fond of them. He wasn't the kind of Captain to just leave his crew to go on his own little cruise.

Many other vessels, including the California-class and Nebula-class ships, also featured Captain's Yachts under the saucer, but others had different support vehicles. A schematic seen in the episode Live Fast And Prosper labelled a vehicle called the aeroshuttle on the underside of Voyager's hull, though it's not clear why the crew never used this vehicle during their stay in the Delta Quadrant. The Nova-class from Equinox was also confirmed to have a similar vessel under it's saucer called the waverider. It was never named in canon, but the waverider was referenced both in Star Trek: The Magazine (Volume 2, Issue 3) and The Official Starships Collection (Issue 15).