How do you retrieve the data to be displayed - an URLConnection? If so, you can set headers to deal with authentication. Check the Applet FAQ -linked in my signature- for an explanation (which is not applet-specific).
Gosh, I never knew you could do that. But it doen't look to me like you can use advanced HTTP features with that method. I would think that it takes no more than 20 lines of code to open a HttpUrlConnection yourself, set the basic auth header, and retrieve the page contents. You could be done with that in an hour.
No, if you call setPage() with a URL, it doesn't seem to allow you to do anything advanced. I'll try the HttpUrlConnection. That sounds like the way ahead.