Hi Jarro,
What part is the broken screw from?
I have had some screws break on me also - very frustrating.
For one I was able to remove the threaded part with pliers,
for another (which broke quite deep and could not be removed with pliers) I had to shift the whole bridge slightly back,
and for another (for a pup surround I think) I actually just CA glued the head part onto the top of the surround (as it was not under a lot of stress and the surround still sat flat on the body top).
EDIT: also, do you use bees wax on the screws before you put them in?