Here's a little tool that knowone should be without. My son bought it for me a couple of years ago and it has saved my you know what a number of times now. There are a number of different models but this is the one I have:
Alden 8440P proGrabit Damaged Screw & Bolt Extractor
Bell shaped drill head helps you stay on center
Works on jagged, uneven and rough breaks – no bolt preparation required
Self-centering drill tip means no walking or wondering
Deep serrated edges – biting action results in greater torque for hard to remove bolts
Quick connect compatible
Removes bolts ¼”, 5/16”, 3/8”, ½”, 6mm, 8mm, 10mm, and 12mm
Use with 3/8” variable speed reversible drill
Drills up to grade 8 and 10.9 class bolts
Also includes a specialty extractor for rusted, hard to remove bolts
http://www.mcmelectronics.com/product/ALDEN-CORP--4017P-/22-10980Those drill outs are nice, but you can get them at your sears store instead of ordering them on line, and they are a bit spendy. They do make a “left hand” drill bit that sometimes will pull the head out as you drill it, they make a thing called easy outs
http://www.brokentap.com/easy-outs.html that every tool box should have. They’re really cheap compared to the drill outs, they cost about $3 at the auto shop store. Just one thing about the easy outs, they’re made of harder metal then your drill bit, so if you break it off in your bolt, you’ll hate yourself! Squirt some “liquid wrench” on the broken bolt when you use the easy outs, that’ll help also.
I’ve sometimes used a nail punch tool on one edge of the broken screw, with a hammer, and at an angle, tapped the broken screw counter clockwise until it comes out. It’s a little tricky, but it can be done.
Good luck, it’s not the end of the world, I’ve done it quite a bit.
