Nodeunit not detecting done()

Question 1

First, I don't know what "server" is in your code, but I would expect it to be asynchronous, so to have something more like this in your setUp function:

function (callback) {
  server.StartServer(function(){
    callback();
  });
}

Second, keep present that nodeunit executes the startUp and the tearDown functions after and before EVERY test so I suspect you are starting your server 2 times (as in the tearDown you are not really closing it).

Question 2

I've spent the last couple of hours messing with this issue, and what has become clear is that nodeunit has no ability to catch and display exceptions thrown in functions which are triggered later by an IO or setTimeout type process. Considering the way JavaScript runs, this isn't surprising. Everything works once you are sure there are no exceptions, but if you have an error in your code, you will get "undone tests" message and nothing else. Here is what I did to resolve my issues (using a restify route as an example):

function myRoute(req, res, next) {
    try {
        // your code goes here...
    }
    catch (err) {
        // write it to the console (for unit testing)
        console.log(err);
        // pass the error to the next function.
        next(err);
    }
}

Once I understood the problem in this way, fixing it because a lot more clear and I was able to get all of my tests to pass!

Question 3

I suspect you're not actually calling test.done() in that second test. Put a console.log() call in there to verify you're actually making that call.

FWIW, I repro'd the described problem using a simplified version of your test, below. If you omit the on('error', function() {...}) handler, then the 2nd test fails to complete. Thus, my theory is that your /push endpoint is triggering a different behavior in the restify module. I.e. are you sure restify is invoking your callback with an err property there, or is it doing something different? ... like, for example, emitting an event like http.get does, below.

var http = require('http');

exports.test1 = function (test) {
  test.expect(1);
  http.get({hostname: "www.broofa.com", path: "/"}, function (res) {
    test.equal(res.statusCode, 200, 'got 200');
    test.done();
  });
};

exports.test2 = function (test) {
  test.expect(1);
  http.get({hostname: "www.no-such-domain.com", path: "/"}, function (res) {
    test.equal(res.statusCode, 200, 'got 200');
    test.done();
  }).on('error', function() {
    // Comment line below out to repro the "Undone tests" error
    test.done();
  });
};

Question 4

I'm working around it by forking the server into it's own process in the setup and then killing it in the teardown. Think the issue was to do with the server being created and not shutdown. Thanks @matteofigus for that.

var cp = null; // child process
exports["tests"] = {
    "setUp": function (callback) {
        cp = fork("./lib/server.js", {"silent": true});
        callback();
    },
    "tearDown": function (callback) {
        cp.kill("SIGHUP");
        callback();
    },
    "CanIHaveSomeTeaPlease?": function (test) {
        test.expect(4);
        client.get("/tea", function (err, req, res, data) {
            test.equal(err.statusCode, 418, "Expected ImATeapot Error.");
            test.equal(err.message, "Want a biscuit?", "Expected to be asked if I want a buscuit.");
            test.equal(err.restCode, "ImATeapotError");
            test.equal(err.name, "ImATeapotError");
            test.done();
        });
    },
    "TakeThisInfo": function (test) {
        test.expect(1);
        client.put("/push", {
            "hello": "world"
        }, function (err, req, res, data) {
            test.ok(false);
            test.done();
        });
    }
};