I looked up my packages reference number. You can either do:
If your order number is W115143163 look up by searching W1151431
If your phone number is (949) 123-4567 look up by searching 9491234567
The phone number is not the phone number of the iPhone you are upgrading or extending the contract. It is the phone number that apple has listed in your Order Status page. Look to the left where it says "Ships To" to find out what phone number to search for.
Make sure your iPhone has shown up in the supportprofile.apple.com before wasting time searching for it. It took my iPhone about 12 hours to go from showing up in the Support Profile, to being able to search in UPS by reference.
Yeah so to further complicate this, I cannot look mine up by shortened order number and my phone number is the one I am upgrading (my billing number) and not my shipping phone number listed on the order.
Maybe try both? I bought mine from the Apple Store via the app.