If you are saying that your "AirPort" is a Time Capsule.......
Hold down the option key on your Mac while you click on the Time Machine "clock" icon at the top of the Mac's screen. Select Verify Backups and run the check
If there is a backup already in progress when you do this, Verify Backups will be grayed out. Wait awhile, then try again.
The process might take anywhere from 10-60 minutes or more depending on how much data is stored in the backup file. Let the process run until it completes, or until you see an error message.
If an error message appears, post back with the exact text of that message
If you want to watch the progress of the diagnostic check, click on the Time Machine "clock" icon at the top of the Macs screen and then click on Open Time Machine Preferences. On newer operating systems this will read Open Time Machine Settings.
Otherwise, you will see an onscreen message that the check has completed.