Don't have a heart! Kill them. Respect and love the mice that stay in the wild, kill the ones that come into your home.
I put a snap trap in a small paper lunch sack and bait it with cheese and peanut butter. The paper bag makes a nice safe hiding place and when you kill the little vermin, you just have to pick up the bag, roll the top shut and throw it away.
Spring traps are only about 50 cents each, and the whole package, bag, trap and mouse corpse is biodegradable, so you can feel okay about throwing them into the woods (just kidding) (sort of ;o)