Comment by scrollaway

BTW, Battle.net Authenticators look nonstandard at first glance, but they are actually 8-digit TOTP. I wrote a Python library and command line utility which can create new Battle.net authenticators as well as generate codes and QR URIs:

https://github.com/jleclanche/python-bna

See the README for usage :)

This should help you to have a backup next time you get locked out!