Here are two Tech Tips that may be helpful:
http://www.stovebolt.com/techtips/bolt_broken_remove.htmlhttp://www.stovebolt.com/techtips/bolt_removal.htmlI like to TIG weld a blob on the end of broken bolts, then let it cool a minute to so, and vice grips on the blob to turn it out.
If it doesn't work the first time try again, nothing to lose or mess up.
I have a very nice set of broken bolt extractors, they work great when they work, but rusted and stuck stuff usually get the better of them. Great for broken pipe fittings and broken but not rusty stuff.
The advantage of welding onto a broken bolt is the heat is concentrated on the bolt, not the surrounding part. The hot bolt expands with the heat crushing and loosening any rust bond, then when it cools and shrinks the then somewhat powdered rust doesn't fight so hard.
If it takes you a while to get it to a welder it can't hurt to start soaking it with penetrating oil now. PB Blaster works well on the kind of rust found on exhaust manifolds/bolts.
Grigg