Lately I have really good luck with broken bolts by welding a washer to the broken piece, then welding a nut to the washer. With this method, you can get a much better bite on the broken bolt or screw with the welder, and you can weld a bigger nut to the washer for a better grip. It helps me since I am terrible at welding through nuts, it always sticks to the nut more than the part I am after.
