I have had pretty good success by placing a caked up muffler over the side burner of my gas grill turning it on high and letting the flames stay on it for 10-30 minutes. Most of the time, the muffler will smoke heavily for a while, and often you can see an internal flame begin in the muffler. After removing from the heat and letting it cool, you should try and make sure no loose carbon comes out any of the openings on the muffler. You could also possibly try blowing compressed air through it, or even running water through it to ensure no solids are left that could get back into your engine.
I've also had some success with a propane torch where I will send flame directly into the muffler inlet and outlet for several minutes to see if I can burn out the deposits. The grill method may take longer overall, but is less hassle.