Aria here, one of the Social Care gurus at Shopify.
Which shipping rate did your customer pay for? Do USPS guarantee it will be delivered in a certain amount of time? If so, you may be entitled to make a claim with USPS but I'd need more information before I can help you find the answers on that one.
Normally, you would refund shipping within the order because that's where the customer paid for it. You would click this button:
You'd then key in the amount and hit the refund button:
I'll look out for your response. Once I have more information, I'll try again to help you.
Jeyfel, I would like to know your experience shipping with USPS. Are you getting frequent undelivered orders/late delivered orders? Are you using insurance while shipping?