Hey Lonerganj8,
It sounds like you're looking to save information from your Apple Watch. We can understand wanting to look into that further. We want to help.
When you unpair an Apple Watch from an iPhone, the Apple Watch data is backed up automatically to that iPhone. You can learn more about that here: Back up your Apple Watch
In order to transfer data from your Apple Watch to your new iPhone, you would need to restore the new iPhone from a backup of your previous iPhone as that would include your Apple Watch backup. You can find more information on this here: How to pair your Apple Watch with a new iPhone
Thanks!