An important point is how the bolt broke off. If it broke from inadvertent overtightening during installation, you will probably get it out one way or another. If it broke off because it was corroded in place, you will not get it out and the solution will be along the lines of drilling and rethreading.
For the ridiculous high-tech approach, you can scout around for a machine shop with a portable EDM http://edmtechcenter.com/index.php/products/hole-drilling/portable-edm-tap-remover. An EDM can burn out the body of the screw and the screw helix can then be picked out.