Removing weld nuts?

[Improbcat]

I snapped a lot of the bolts holding my front end together, and it seems like it would be simpler to remove the weld nuts with the bolt halves rusted into them and weld on new nuts than try and get the broken bolt out.
To that end, does anyone have any good tricks for getting the weld nuts off the panels? Some are easy to grind off, but a couple are in locations that getting at the weld nut on the back is going to be a challenge.