I do not think that there is a direct way to do this. For example, I could write my own URL shortener tomorrow - and since the shortURL->longURL mapping is private, on my server, I would need to provide you with a way to access that information.
So if you have control of the website, you might be able to glean information from looking at the server logs - the REFERER header, in specific.
I know that for bit.ly, it would be easy for you to shorten the URL there, and that would give you its corresponding shortURL. This same short url is used for anyone who uses bit.ly, unless someone has registered an account.