Ayear ago last April, my wife & I were flying from SFO to OGG for a 10 day holiday. We vwere waiting for the flight to start boarding, and all the gate board said was "delayed"
with no time. the aircraft (UA 757) was parked at the gate.
Finally, the gate agent came on the P.A. and said the delay was due to a mechanical problem, and that the pilots would have to take the plane up for a quick "test" and if it was o.k., we would go off to Maui.
They backed out, took it up for a 5 min turn and returned to the gate. They pronounced it "ok to fly" and we were ready to board.

I must admit we were a bit nervous as i had never seen this done before. I assume it was a minor problem that would not affect safety, but it was still a bit nerve wracking!
The good part was there were only 30 passengers on board, so it was like a private jet to Hawaii- everyone got to move into E+ and they gave us free booze all the way!
^