...And while they'd pull on each other, I'd think the interaction wouldn't much resemble the Earth-Moon kind of mutual orbiting. Both the ship and the station would be more affected by the distant planetary or stellar body that they were co-orbiting, and would weave their individual orbits around that body in an interesting braid that wouldn't look like a neat and tidy ship-ellipse-around-fixed-station setup even from a close-up, moving reference frame.
However, artificial gravity could certainly be created for this purpose of securing a ship to the vicinity of the station. Doesn't sound like a worthwhile endeavor, though. If one wanted to stabilize a ship via tractor beams or directional gravity, wouldn't one prefer to secure her in place, rather than in an orbit-like track?
I guess the two ships orbit K-7 in "Trials and Tribble-ations" not because they have to, or even because they can - but solely because they don't want to appear too passive to the opposing ship. They don't want to power down or settle in place; they want to remain ready to pounce. Doing that little dance helps them the same way it helps a boxer...