How do I loosen the screw on the underside of the faucet handle if the allen wrench didn't work?

Please do not double post.

There are several things that you can do.
1- Drill it out **or**
2- Take something with a small thin blade and see if you can wedge it in the Allen and head screw. Then back it out counter clockwise. Good luck. Tom

For loose fitting allen wrenches, I've had luck wrapping the end of an allen wrench / key with a small square of aluminum foil...

For loose fitting allen wrenches, I've had luck wrapping the end of an allen wrench / key with a small square of aluminum foil... Outstanding!
Thanks Mike for your solution. You just taught this old dog a new trick. Tom