I do have perfect pitch. My brother does not. He has absolute pitch, or maybe relative, can't remember which is which. He can hum a B flat in his head perfectly. He is a clarinet player, so in high school and college band the tuning note was B flat. He got that note engrained in his mind. From there he can figure out what key a song is in by counting half steps in his head. He is dead accurate 75 to 80% of the time, and only a half step off the rest of the time. This is your best bet for being able to do it. Get one key so solid in your head that you can hear it in your head without actually hearing it, then just think half steps up or down from there.