I did exactly this! All I get is a message in red reading that it could not be found or whatever.
Who asked if I got a serial number? Where do I get a serial number?
Look on page 1 of this thread, there is a link to your support profile. Your profile has a list of registered devices, including the new iPhone if its been allocated to you yet.
If your new phone is not listed, they haven't set aside a phone for you yet, so it won't have a UPS label or tracking number.
There are several folks monitoring this thread that are in the same boat.