There are several places you can find your goggles' serial number if needed.

1. If your goggles are already paired to your app account, you can see the serial number by opening the app and navigating to My Goggles then Goggles Settings. 
2. If you still have the original packaging, you can find the serial number on the end of the gift box with the barcodes on it. Near the barcode, you will see a number that starts with a J or a Y: this is the serial number.
3. The serial number is also printed on the goggles. For Smart Swim 2, it's on the inside of the lens near the tech pack.

For Smart Swim 1, it's on the underside of the goggles' display module. It may be tricky to see but pulling the plastic slightly should reveal the number. The below image shows the area circled in red.