Without using ROT13 explicitly, it can be done. You can draw up a frequency histogram of the text, and then shift it 13 characters left (or right). If it lines up to give the average English frequency distribution, it's likely this is ROT13 material. This will only work well if you have a large enough sample, obviously.
You should be able to do roughly the same thing with Base64, since it too preserves frequencies to some extent (though in a less obvious way, as the encoding works at the bit level, not on each character)
Though for Base64 a more intelligent approach is to just decode the whole thing and check that it looks like english (or whatever format you expect, really) either by frequency analysis or another method. It would be much faster and easier, but according to your question this is not a valid approach, so...
Nitpick: neither ROT13 nor Base64 use a cryptographic key, so they are not ciphers, but encodings (at least Base64 is - ROT13 tries to be a cipher, and could be called one, I suppose, but it's not technically correct).