Hello, B J -
Instructions for registering your watch start on page 20 of the watch instructions (see the PDF document, Adobe Acrobat Reader software needed - free):
Apparently, the watch serial number is printed on the watch packaging. You may not have kept that. Or, you may not have purchased the watch from an authorized dealer.
If you find you need the watch serial number to register your purchased watch, it may be located inside the watch battery compartment.
NOTE: The instructions for your model watch state the following:
WARNING Do not attempt to open the Neo+ Watch. Risk of explosion if battery is replaced with incorrect type. •Do not attempt to open, disassemble or service the internal battery. The battery must be replaced by a qualified technician.
Visit a jewelry store and ask one of the store employees to open the watch back and look in the battery compartment for a number.