Griswold is among a small, but growing number of elite passengers picked by Delta Air Lines to get a VIP escort from one flight to another in a Porsche at Atlanta Hartsfield Airport.
The criteria: Diamond Medallion Status travelers – those with at least 125,000 frequent flyer miles – who have connecting flights that they may have trouble making.
The Delta Elite Services team reviews flight manifests every morning to find passengers who meet the criteria. Then, unbeknownst to the travelers, they show up at the plane with the Porsche when it pulls into its gate in Atlanta.
"[When] they look out the door and see a Porsche sitting there. It really turns their frown into a smile," said Cousin.
Amy Plaxton, an audiologist heading to Tampa, Florida to meet a patient, couldn't believe it when her flight from Omaha, NE touched down in Atlanta and she found herself escorted down to a Porsche waiting on the tarmac.
(Read more: Owner of flaming Tesla defends the car)
"It's the busiest airport in the world so you have to do a lot of weaving in and out as you go through the terminal," said Plaxton. "I mean here we are, almost a limo service to my next airplane. So yeah, that's fantastic."
Tarmac Escorts Expanding
The creation of tarmac escorts at hub cities is airlines' latest attempt to take care of their most elite customers.
This month, Delta will add tarmac escort service to its hubs in Minneapolis and Los Angeles. After that, the program will target customers at JFK airport in New York.
"Those frequent travelers – the super-high value folks – [that's] where we can differentiate the most," said Mike Henney with Delta Air Lines.
Meanwhile, United Airlines has started its own elite customer tarmac escort service at O'Hare Airport in Chicago and Houston International Airport.
United's program, which started in July, targets Global Service members of its frequent flyer program. Only a small percentage of United's frequent flyers attain Global Service status and like Delta, United does not notify people in advance when they will be picked up.
With other hub cities like Washington, Dallas and San Francisco handling more flights and more frequent flyers connecting through those cities, don't be surprised if more airports add this type of escort service.
Beating Packed Terminals
When Wayne Kinney was escorted off his Delta flight from Evansville, Indiana he loved the idea of getting picked up in Porsche Cayenne.
(Read more: Inside the battle to dominate the US auto market)
The idea of driving just a few minutes to his next flight instead of fighting the crowds to go between terminals really appealed.
"It's different on these side roads and stuff, but it's a lot better than trains, walk ways, jet ways, and that kind of stuff," said Kinney.
Bill Dickerhoff, another frequent flyer driven across the tarmac by the Delta team, agrees
"It's a very comforting feeling," he said. "It feels like the airline cares."
—By CNBC's Phil LeBeau; Follow him on Twitter: