If you control the compiler, you don't need the engine's support for exceptions (though you might want it for performance reasons) - emitting function prologues and epilogues that maintain debugging information like a call stack (or call trace in a ring buffer like some Schemes) would be one way.

I actually did this in my purely functional language, but had it off by default for performance reasons - if you hit an error at runtime, the debugging code would re-execute from the last checkpoint with debugging information turned on to construct the missing debug data, something I could only do because the language is side-effect free.