You essentially have two options:
1. Abstract the call to the framework and test this.
E.g. refactor the code to allow you to inject a mock implementation at some point. There are many ways to do this. e.g. create a getUrlAsString() and mock that. (also suggested above). Or create a url getter factory that returns a GetMethod object. The factory then can be mocked.
2. Start up a app server as part of the test and then run your method against it. (This will be more of an integration test)
This can be achieved in an number of ways. This can be external to the test e.g. the maven jetty plugin. or the test can programmatically start up the server. see: http://docs.codehaus.org/display/JETTY/Embedding+Jetty
Running it over https will complicate this but it will still be possible with self signed certs. But I'd ask yourself - what exactly you want to test? I doubt you actually need to test https functionality, its a proven technology.
Personally I'd go for option 1 - you are attempting to test functionality of an external library. That is usually unnecessary. Also it's good practice to abstract out your dependencies to external libraries.
Hope this helps.