How to test enum types?

I'm currently trying to build a more or less complete set of unit tests for a small library. Since we want to allow different implementations to exist we want this set of tests to be (a) generic, so that we can re-use it to test the different implementations and (b) as complete as possible. For the (b) part I'd like to know if there is any best-practice out there for testing enum types. So for example I have an enum as follows:

public enum Month {
    January,
    February,
    ...
    December;
}

Here I want to ensure that all enum types really exist. Is that even necessary? Currently I'm using Hamcrests assertThat like in the following example:

assertThat(Month.January, is(notNullValue()));

A missing "January" enum would result in a compile time error which one can fix by creation the missing enum type.

I'm using Java here but I don't mind if your answer is for a different language..

Edit:

As mkato and Mark Heath have both pointed out testing enums may not be necessary since the compiler won't compile when you are using an enum type which isn't there. But I still want to test those enums since we want to build a seperate TCK-like test.jar which will run the same test on different implementations. So my question was more meant to be like: What is the best way to test enum types?

After thinking about it a bit more I changed the Hamcrest statement above to:

assertThat(Month.valueOf("January"), is(notNullValue()));

This statement now throws a NPE when January is not there (yet). Is there anything wrong with this approach?