The easiest, most likely to succeed, and best chance of not ruining the threads is to weld a nut to the bolt and then unscrew it.
I find that drilling is going to lead to damaged threads most of the time, as it is hard to be centered and parallel to the centerline of the bolt. I only try drilling first if you don't mind installing a Heli-Coil if things go badly.
The best way to remove a broken bolt by welding is with a TIG welder. You can build up the bolt first if it is broken down in a hole. Then once it is flush you can either continue to build it up and use vice grips to remove it, or weld a nut to it from the inside of the nut and use a wrench.
A MIG welder can also be used, although it is much more difficult if it is below flush. If it is flush first place a washer over it that will just show the bolt but cuvers the threads so they are protected from welding, an under size washer for the bolt. Then weld the washer to the broken bolt. Then weld a nut to the washer and remove.
A stick welder can also be used with the same method as the MIG welder, but it is tricky to do on small bolts. I have seen special rods for welding broken bolts that are down in a hole, the flux protects the threads while you weld a tower on the stud to get it up out of the hole, much like if you were TIG welding. I can get info on these if anyone is interested, but I have not used them.
The reason welding works well is because the heat from the welding will expand the bolt and crush the rust around the threads, then the bolt cools and shrinks, leaving it a little looser in the hole than before. Welding will also un-Locktite a bolt.
Grigg
