It depends on your organization.
With NAUI, SSI, TDI/SDI & IFDI, you can prove your diving level through a web page.
You can find all useful direct links to those pages on ifdi.info divers page: https://www.ifdi.info/Divers.php.
With PADI, you may download their application.
With other diving organization, it does not seem so simple...
Is there some of you who knows how to proceed in those other diving organisation?
Best regards.
As an aside to this thread, before I travel I take pictures of all the documents I'm going to have with me (credit card, drivers licence, passport etc but also insurance info and soforth) and then paste them all into a PDF file and email it to myself on gmail. Pretty much where ever you go in the world these days you can get on the internet so even if you get robbed down to your skivvies you still have access to your most important travel documents.
I know this isn't what happened here but I just wanted to throw that out there.
R..
---------- Post added September 4th, 2015 at 12:46 AM ----------
BTW, a PADI shop will be able to look up your card info based on your name and birth date provided to you remember the exact way it was printed on the card.
R..