As others have said, a spy network of ecclesiasts is very effective, I used to try emmisaries, it made more sense, but they attract assassins very fast.
If you hide away and don't rampage across the map, you tend to end up facing 1-2 large empires in Late, if they're of a different religion, the religious revolts kick in, along with normal "imperial overstretch" rebellions and you can collapse your enemies with a few swift assassinations to promote a full blown civil war. I love doing this as the Byz, it just seems to make sense somehow.