Don't test that something doesn't happen. It's like assuring that code doesn't break. That's sort of implied, we all strive for non-breaking, bug-less code. You want to write tests for that? Why just one method? Don't you want all your methods being tested that they don't throw some exception? Following that road, you'll end up with one extra, dummy, assert-less test for every method in your code base. It brings no value.
Of course, if your requirement is to verify method does catch exceptions, you do test that (or reversing it a bit; test that it does not throw what it is supposed to catch).
However, the general approach/practices remain intact - you don't write tests for some artificial/vague requirements that are out of scope of tested code (and testing that "it works" or "doesn't throw" is usually an example of such - especially in scenario when method's responsibilities are well known).
To put it simple - focus on what your code has to do and test for that.