The expression "I can bear witness to that" is spoken several times in Act III by a couple of different characters. The action centers around some missing jewels. Constance has asked Mrs. Hardcastle's permission to wear the jewels that are rightfully hers. Mrs. Hardcastle doesn't want to give them up, so Tony tells her to say they're missing, and he will "bear witness" that they are gone. He means, "I'll back you up" or "You're right about that."