What awards did William Shakespeare win after death?

None. Oh, he was given nicknames, like "the Bard", or "the Swan of Avon" but these are not awards like the Pulitzer or Nobel prizes or the Academy Awards. They didn't have such things in Shakespeare's day. The closest he got was getting a coat of arms for his father which he inherited and was very proud of, but Shakespeare's career as an actor was an impediment for such an honour, not the reason for it.