Testing is not actually about ensuring correctness; it's about discovering mistakes. The only successful test is one that fails, and thereby reveals a bug.
To use testing effectively, it's vital to get into the right (i.e., slightly counterintuitive) mindset when writing tests. You need to get to the point where you're mildly disappointed if the test suite runs without reporting a problem.
The logic behind that disappointment is simple. All non-trivial software has bugs. Your test suite's job is to find those bugs. If your software passes your test suite, then your test suite isn't doing its job.
Of course, at some point in the development process you have to decide that the code is finally good enough to deploy (or ship). And, at that point, you definitely want that code to pass its test suite before you send it out. But always remember: it's passing the test suite because you decided you'd found all the bugs you cared to test for, not because there were no more bugs to find.