Make sure you remove all the bobbin hardware such as studs, screw or various polepieces. The best way I found to get out broken screws in humbucking bobbins was to carefully heat the broken screw from the bottom with a pointed soldering iron (not gun) to soften the plastic around the threads. From the top of the bobbin I insert a paper clip while heating the screw till it’s hot enough to be pushed out. If enough of the screw extends from the bobbin try filing it flat and file a small slotted groove into it, then try to unscrew it. You can try to grab the broken screw with needle nose pliers or wire cutters but this can often strip the screw making it harder to remove. I still like the soldering iron trick to loosen screws in the tight holes. You can usually remove the screw with little damage to the bobbin. If the screw is broken off way in side, I insert a small drill bit through the bottom to conduct the heat to the broken screw. If the bobbin has no holes on the top to help push the screw out the bottom I drill a fine hole in the top of the bobbin directly above the broken screw and again use a paper clip to push the heated broken screw out. This can be difficult and should be done by an experienced repairman. Be careful not to touch the hot screw with your fingers and make sure you wear eye protection.

1. Remove all bobbin hardware such as studs or other polepieces
2. Mount the bobbin securely in a small vice or clamp
3. Carefully heat the shaft of the broken screw
4. Insert a small paper clip from the top side of the bobbin through the same hole as the screw and push the broken screw out towards the bottom of the bobbin
5. If no hole exists at the top of the bobbin, then the broken screw will have to be pulled out by fine needle nose pliers or wire cutters that can grab and hold the screw.
6. I dampen the hole on the bobbin to cool it down quickly
7. Be careful the hot screw doesn’t fall on a surface that can be easily damaged.