We had an infestation of mice when my young son was staying with me a lot, and as we both care about animals, I had no choice but to go the humane way. I tried a commercial humane trap which didn't work at all.
So I made my own. I inverted an old bread bin and propped up one end of it using metal rod that was about 2 inches long. Then I made a "trigger-mat" out of a couple of sheets of cardboard with some wires carefully taped between them, and put it under the bread bin, so that when the mouse walks onto the cardboard mat, the wires connect together. Next, I connected this rudimentary swich to a small electric motor and a battery, so the mouse turns on the motor when it trips the switch. I wrap a piece of thread round the shaft of the motor and fasten the other end to the metal rod that's propping up the bread bin. Put some bait at the centre of the mat.
See what happens? The mouse walks under the bread bin and triggers the switch, which turns on the motor, which winds up the thread, which pulls the metal rod out, and the bread bin closes. Next morning, carefully slide a thin sheet of wood under the bread bin, lift both together and invert so the bin is the right way up. Take the closed bin well away from the house and release the mouse.
We did that for a few days and that was the end of the trouble. There was a sad accident one time when the mouse got squashed under the wall of the bread in (the switch had tripped too early), but at least it looks like it had a quick death. Better than dying of Warfarin poisoning, that's really a bad way to go.