[Spaceships] How should a large station... duck?

[Ulzgoroth]

Originally Posted by Donny Brook

Place it in mutual orbit with a tethered counterweight. To dodge, reel out more tether.

If you can manage a really big megastructure, you can one-up that by having a counterweight-and-cable system that wraps around the star and lets you adjust your orbital radius. Over lengthy projectile flight times that should let your orbital period be unpredictable so they basically have to search the entire orbit for you during the approach.

(If you don't mind being unsubtle, putting a big opaque cloud of satellite/statite objects around the system so the attacker can't see anything until they get very close is a possibility, but it sounds like security-through-obscurity is wanted here and being a blatant astronomical anomaly might hurt that.)