MacBook Air 13 was stolen, need to recover serial number

If the following are true, then you can see the map location of your MacBook Air, lock it, and even erase it, providing it is powered on, and has not had the drive wiped and operating system replaced:

1. System Preferences : iCloud : [√] Find my Mac
2. System Preferences : Energy Saver : Power Adapter : [√] Wake for Wi-Fi network access
3. System Preferences : Security & Privacy : Privacy : Location Services : [√] Enable Location Services

With these settings, you can sign into iCloud dot com and select Find My iPhone. Top, center screen is an All Devices selector, and you would pick the name of your Mac. If it is on, you should see a map of its location, which you can share with the police. Also, superimposed on the map, and in the upper-right corner will be the following, which in my case, shows my 2014 MBA on battery:

Fortunately for me, the MacBook Air is right next to me.

Check in your Apple ID account > listing of your devices. Or, check the original purchase receipt.