There is a chance of looting artifacts at the end of a siege. Warrior lodge ranks and some bloodlines can be used to increase this chance.
But the primary method I use is inheritance. In general, if an unlanded courtier dies then his liege has a fairly-low chance to inherit some or all of his artifacts.
A couple of clarifications on inheritance:
(1) It is the liege that inherits, not the court that the unlanded character happens to be in. If a prisoner dies but he is not your direct subject, then you can't inherit his artifacts.
(2) Artifact inheritance is weirdly distinct from gold inheritance. You only inherit a courtier's gold if he dies while having no living parents, siblings or children. However, a courtier's artifacts always either disappear or are inherited by his liege.
So, use the character finder to find an unlanded character with the desired artifact. Get him into your court somehow. Then kill him. If you don't get lucky and inherit his artifact, try again with another unlanded character. (Alternatively, you can savescum. If you choose this, it's best to wait a few months between attempts.)