Do you think that you could show them the serial number available through this "About this Mac" menu by clicking twice on the Mac OS version in the palette that appears?

After all, faking a serial number in a program is as easy as faking a sticker with a barcode on it so security checkpoints may accept it...

Another option would be to print a sticker with your serial number yourself, provided that it's allowed... Bar code fonts could be of help.

F.J.