If one or more assassins are loitering near to one of your cities or armies, and you have no assassin of your own to deal with them, the manhunt method may be helpful and fun. It's most effective if there is a river or some impassable terrain close by, but can work without this.
You move units one by one to form a close-spaced cordon around the assasin and hem him in. Once all gaps through which he might walk away are closed, you move another unit to where he is standing, when, all being well, he is caught by your searching troops and they finish him off.
Spies too can be dealt with by a manhunt.