If this was my code I would extract the Calendar variable into another method, overloading the method so that there is one version that takes the Calendar as a parameter and one version with no arguments, like this:
public static String getDate() {
return getDate(Calendar.getInstance());
}
public static String getDate(Calendar cal} {
// your example code
}
This way you can write tests exercising your logic in getDate without having to use any mocks. If you really want to cover the no-args version of the method then you can use PowerMock to mock Calendar's getInstance method (here's a question with examples of that).