Here's my simplified version of Toby's original solution. This solution takes advantage of Jasmine's built-in toThrow() matcher which is similar to matchers in the should.js, expect.js, and chai assertion libraries which all work with Mocha.

omit-callback-unit-test.js

// node module
var assert = require('better-assert');

/**
 * make something
 *
 * @param {Function} callback(err, something)
 */
var makeSomething = function(callback){

    var something = 1;

    if (arguments.length >= 1){

        something++;
        callback(err, something);

    } else {

        // nothing = fail
        // do not throw error = fail
        // do not throw custom error message = fail

        // throw custom error message = pass
        throw new Error('Missing parameters');

    }

};

describe('makeSomething()', function(){

    it('should be a function', function(){

        assert(makeSomething !== undefined, 'must not be undefined');
        assert(typeof makeSomething === 'function', 'must be a function');

    });

    describe('making something to callback to nothing', function(){

        it('should throw a meaningful error', function(done){

            var err;

            try {

                makeSomething();

            } catch(e){

                err = e;
                assert(err !== undefined, 'must throw a catchable error');
                assert(err.toString() !== 'Error', 'must throw a meaningful error');

            } finally {

                assert(err !== undefined, 'must throw an error');
                done();

            }

        });

    });

});