[Geoff]

The problem is the stud is very likely rusted in place. So not only are you trying to remove a bolt that is tight, it is also rusted in there.
There is an electrical process that will remove the broken stud. I had some broken exhaust studs in a b/b Mopar head many years that were removed with this process. I took the head to this place that specialised in removing broken bolts/studs. I am not 100% sure how the process works, but I believe the broken piece is subjected to a strong electric or magnetic field that causes the piece to 'vibrate' & loosen.

[JackMonkey]

Another tip:

If the stud breaks off flush and if the drill bit wanders, I use progressively larger bits until I just start to hit the threads on the manifold. Then take a pick or drift punch and start bending in what is left of the stud closest to the manifold. There should only be the high part of the threads left so the stud isn't very strong at this point. After a while you will basically cave in one side of the stud and you can either unthread it or push/pull it out of the hole. It takes a while but has worked for me.

I hope that made sense.

[RARON455]

I paid my local machine shop 15 dollars to fix the one on my z-28, Trust me cussing the thing dont work!!!!

[Jack Gifford]

Originally Posted by Geoff

There is an electrical process that will remove the broken stud...

You're probably referring to EDM- Electrical Discharge Machining. It's a good alternative to know about, and a fair number of machine shops have the capability. There are a few limitations (shape of part, etc.) and it's not real cheap, since it's very time-consuming. But if you're ever stuck with a high-value part that has, say, a broken-off tap in it, it's just about the only choice.