I like the technique that this guy uses to extract bolts that have broken off inside of a recessed hole.
Spoiler alert! I'll explain the technique after the link if you don't want to watch the video.
... ... ... ... ... ... ... ... ... ...
Spoiler:
He drills a hole through the center of a cap bolt, screws it in and then locks it down with a jam nut. Now he has a drill guide so that he can drill a dead center hole in the broken bolt for a screw extractor.
For smallish holes, he use a Vix bit to center the drill bit.