The only thing that would really be helpful and the only place Apple doesn't provide it is on the back of the iPhone itself .. Always wondered why that is?
U can derive from the MEID, or IMEI instead,, but Apple seems to use that only iin the places u cannot get at the serial number easily (etc.. in the SIM tray for example , but u need to get it open first) if u don't have anything pointy with you.