Send an empty envelope addressed to them at their old address and write on it "Return Service Requested". The post office will then deliver the envelope back to you with their new address if they have put in a forwarding address. Make sure you have your return address clearly marked on the envelope.
Please go to the USPS.com website and read the exact directions on where and how to place the "address service requested" to get the fowarding address of the tenant returned to you on a postcard. Yes, the envelope will be forwarded to the tenant; the postcard notice will be provided to you. In my area, it took 3-4 weeks for the card to be sent to me. There are other notification options, you can read about them on the USPS.com website.