If you iPhone is in the Completing Activation state and you haven't yet received an email with an order number, check your spam folder. This email was received 15 hours and 6 minutes from the time the activation was submitted.
Subject: Thank you for your recent purchase
We are currently processing your order. Your order number is XXXXXX
You will receive an additional e-mail when your order is complete that will provide further instructions to activate your iPhone.
BTW, after this email was received, our old phones were no longer active.