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Now boarding at Gate 1: Your dogs, cats and other small pets

American Airlines’ pet cabin
Source: American Airlines
American Airlines’ pet cabin

People fly first class, so why not pampered pets?

That's the idea behind the specially designed travel compartments designed for small dogs and cats on select transcontinental American Airlines flights popular with business travelers and entertainment industry VIPs.

The pet cabins—two per plane—are at the front of the first-class section of the 17 Airbus 321 aircraft the carrier uses on flights between New York's JFK International and both San Francisco and Los Angeles International Airports.

The planes' full lie-flat seats in first class don't allow for under-the-seat storage of a pet carrier during takeoff and landing. Still, "we knew the clientele on these flights would love the ability to travel with small pets in that cabin," said American spokeswoman Barb Delollis. "So during the design process, our team created a ventilated compartment certified for a pet carrier."

For $125 each way, passengers booking first-class tickets may reserve a pet compartment for their furry companion. While pets traveling first class on these flights won't get an amenity kit, Champagne or an oxygen mask in case of emergency, their tickets cost the same as those pets traveling under the seat in coach.

"Obviously, the airline understands the needs of their [first-class] passengers and has compromised by allowing a special space for their pets," said Susan Smith of PetTravel.com. "I think it's great."

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It's not just first-class passengers who want to travel with their pets. Eighty million U.S. households now have pets, and a growing number of those animal lovers now take their pets along when they fly.

None of the domestic airlines contacted by CNBC would divulge how many pets they ticket as carry-on passengers each year. However, each has a formal program and detailed policies for how to get a pet on a plane, at prices that can top $125 per pet, each way for a domestic trip.

For each animal allowed, the airlines list charges, size and weight restrictions for pets and pet carriers, and required travel certificates.

Frontier Airlines, for example, charges $75 per pet carrier each way and allows cats, dogs, rabbits, guinea pigs, hamsters and small household birds on board. Although each passenger may only bring aboard one pet carrier, there is no limit placed on the number of pet carriers allowed on each flight.

Southwest Airlines only allows dogs and cats as carry-on passengers, charges a $95 pet fare each way and allows up to six pet carriers on each flight.

"We began offering this service in 2009, and passengers really appreciate this service. We find that the numbers go up around the holidays and during the summer travel season," said Southwest spokeswoman Michelle Agnew. Southwest also sells its own carry-on compliant pet carrier ($58) online and at the airport counters.

Watch your manners, follow the rules

Marco Feldhoff with Cuddly the cat at Frankfurt International Airport
Source: Marco Feldhoff
Marco Feldhoff with Cuddly the cat at Frankfurt International Airport

The charge for in-cabin pets on United Airlines—cats, small dogs, rabbits and birds—is $125 each way, with an additional $125 charge for each stopover of more than four hours on domestic flights.

While some passengers take their pets out of the carriers during a flight, Barbara DeBry of PuppyTravel.com urges her clients to follow airline rules that require pets to remain in their carriers the entire flight. Otherwise, it could make for a rather unpleasant experience.

"There was a recent incident where a woman refused to put her dog in the carrier and ended up being removed from the flight in handcuffs," said DeBry, "She may have ruined it for everyone else."

For those whose pets are too big, too unruly or otherwise unsuitable to travel with you as in-cabin passengers, there are other options. Pets can travel as checked baggage or as cargo, with an escort or courier service. If your budget allows, you can also fly by private jet.

"We work with charter services, which are quite expensive," said Susan Smith of PetTravel.com, "but we're aiming toward shared charters to bring the cost down."

An option in the future might be transporting an animal on its own via an airline that only carries pets.

Pet Airways flew about 9,000 pets on small Beechcraft 1900 twin turbo-prop planes between 2009 and 2011, but ceased operations, "because of the Great Recession," company founder and CEO Dan Wiesel told CNBC. "We were not able to tap into enough capital to survive. We were close, but not close enough."

Wiesel says he's working on resurrecting the airline now. "The economy is good, and pet parents still want an alternative to flying their pets in cargo. The only thing missing is the money to restart the service."

—Harriet Baskas is the author of seven books, including "Hidden Treasures: What Museums Can't or Won't Show You," and the Stuck at the Airport blog. Follow her on Twitter at @hbaskas . Follow Road Warrior at @CNBCtravel.