Usually after an unsuccesful battle you have 1 or 2 units with very few people in them. Send them out to harass troops marching to the gate so more of them get killed before they reach it or try and destroy artillery with them.

Everyone in a siege gets killed, so if you want to save your prince or a good general, it is a good idea to deploy him outside the wall then set him to flee once he is pinned against the wall by enemy units. You can then ransom him back. Otherwise always put 1 unit in the ring wall around the keep and the rest of your army guarding the first gate so more of the enemy get arrowed and have boiling tar poured on them. You will have to decide whether to put your general at the first gate or next to the keep.