Tenants don't want to move out after 60 days

we gave 60 days notice to ask my tenants to move out by 6/15. But he has been trying to come up with many reason to stay after 6/15. He just told me he applied for another house to move in on 7/1, implying to stay until 7/1. What should I do in this situation? I can give him extension to 7/1, but worried if he is serious. How should I charge him if he stays? Can I charge high daily rates? Thank you for your advise in advance