Options to meet this requirement:
In every case below, use a sealed envelope.

When you can or when the risk dictates [sensitivity, number of records], choose hand delivery or ensure tracking/delivery confirmation. Ensure that you put in a mailbox or FedEx box as opposed to leaving in a basket in an open area for someone else to do so.

-Hand deliver (make sure you hand it to the intended recipient )
-University mail (up to Level 3)
-US Mail (use tracking/delivery confirmation where practical)
-FedEX/UPS (use tracking/delivery confirmation)