Well, the most obvious answer would be another unbreakable vow, but I'm not sure that I believe Rowling would use the same device twice. Dumbledor says that it was the biggest regret of Snape's life, but that tells us nothing about what he did to redeem himself. In order for Snape to have received the position he held at Hogwarts you can bet Dumbledor would have needed something significant as proof when he recanted. It will be interesting to see what it was, because I have no clue at the moment.