As suggested here, QUnit could be extended with a

raises

The attached patch allows writing tests like the following:

var expression, expected;

// should pass
expression = function() { return foo.bar; };
expected = "TypeError";
throwsEx(expression, expected, "invalid property access raises
TypeError exception");

// should fail
expression = function() { var foo = {}; return foo.bar; };
expected = "NoneError";
throwsEx(expression, expected, "property access raises NoneError
exception");

(Note that these tests use closures to wrap around the expressions which are actually being tested.)