Extracting a broken drill bit?

[Connectamabob]

So yesterday while I was drilling the pin hole in the mating surface of a figure's arm, the bit snapped off in the hole. Now I've got a length of tiny drill bit stuck in there with the broken end basically flush with the surface. I need to get it out, because the arm isn't wide enough to simply drill another hole. For reference this is the figure in question:
http://www.coolminiornot.com/shop/miniatures/enigma-miniatures/massive-darkness-1/eduhin-morning-star.html

The drill bit is in the proximal surface of the joint (those ringlets on her left bicep mark the join), so drilling in from behind would mean having to drill all the way through from the opposite shoulder, and I don't think I can aim precisely enough to do that and meet up with the broken bit at the end. It was an expensive mini, and to be frank, a pain to clean as the casting was a bit rough, so I'd rather not have to start over with a new one if I can.

Is there a way for me to extract the bit without doing too much damage to the figure?

[revford]

If you're lucky, you may be able to slip a pin in and lever it up enough to pull it out with tweezers.

If it's still got a solid grip or bite on the metal, you'll need a more cunning plan that mine.

[Cory]

On larger bits I usually use a 2 part epoxy glue something to the broken bit and then (after the glue has really dried/bonded) carefully twist out the broken bit.

[WillieB]

Cory has given you the best probable method. However, first put the item in a freezer for a few hours. The steel drill bit will shrink a lot more than the surrounding white metal.
After freezing, first try a strong neodymium magnet if you have one. Sometimes the drill bit 'pops' out just enough to grab with tweezers or pliers.

[gamer Mac]

Some times you can be lucky and try un-screwing the broken drill using a sharp needle file. You may need to open up the hole to get the file in.

[Trysop]

In the past I have managed to use a spot of blue tack on the end of a cocktail stick. I jammed it into the hole and turned it anti clockwise to help work the bit out a little. Then I used clippers to get a good grip to pull out the broken bit turning the mini as I pulled.

I could never manage to get tweezers to grip well enough to pull out a broken bit.

Good luck

[Connectamabob]

Thanks for all the replies.

I tried the freezing and magnet trick, but it didn't work. The freezing didn't seem to loosen the bit any, and the bit was too small to generate any real pull with even one of those super strong rare earth magnets. While it was still cold, I tried wedging first a needle then an exacto blade tip into the threads so I could hopefully pry it up a bit, but that didn't work either.

I ended up breaking out the Dremel to excavate a trench from her armpit to the joint, and extracting the bit laterally. Her arm's basically hollow now, and I'll have to backfill it with JB weld and spackle over with putty before redrilling. Not outside my skill level, but a right pain in the mivvonks none the less.

Guess now I'll have to make certain all that was worthwhile by doing an extra spiffy job on the paint & base.