You can only capture enemies if they are routing. Defenders in a siege will never rout, as long as they are within the castle walls. So, the only way to capture the King would be to somehow entice him to sally forth and fight you outside of the castle. Or autocalc the battle. Kind of dumb, I know. On the flip side, sieges are a great way to increase your general's personal valor, because all of the enemy will fight to the death...