<p>My university doesn't support the POST cgi method (I know, it's crazy), and I was hoping to be able to have a system where a user can have a username and password and log in securely. Is this even possible?</p>

<p>If it's not, how would you do it with POST? Just out of curiosity.</p>

<p>Cheers!</p>

You could use HTTP Authentication, if supported.
You'd have to add SSL, as all methods, POST, GET and HTTP Auth (well, except Digest HHTP authentication) send plaintext.
GET is basically just like POST, it just has a limit on the amount of data you can send which is usually a lot smaller than POST and a semantic difference which makes GET not a good candidate from that point of view, even if technically they both can do it.
As for examples, what are you using? There are many choices in Python, like the cgi module or some framework like Django, CherryPy, and so on