How can I prove to an airline that the iPad mini they found is the one I left on the plane, without giving them the passcode?
If you have your iPad's serial number it should be visible on the back of the device.

source: Apple

As mentioned in the comments below, you can get the serial number by either:


Logging into the AppleID associated with the device at appleid.apple.com.
In the Apple ID area in the Settings app on your iPhone logged into the same Apple ID. (The very first thing if you scroll to the top of Settings.)