Claudio and Don Pedro meet in the churchyard at Hero’s family tomb.
Claudio has brought with him the epitaph that Leonato asked him to write. He reads it aloud, and it basically says (in kind of poor rhyming) that Hero was put to death by slander, and Death will try to compensate for her wrongful passing: though her life was ruined by shame, her death will be marked with fame (he’s as bad as Benedick).
Then there’s more singing about how Hero was a virgin knight of that virgin goddess, the moon. Claudio announces he’ll come to Hero’s tomb and read (bad) poetry every year.
Don Pedro notes that the sun is coming up. It’s about the hour when they should go off and change out of their funeral clothes and into some wedding clothes, because it’s party time!
They exit, with Claudio being like, "Man, I hope this goes better than the last time I tried to get married, like two days ago."