LOS ANGELES — Gigi Griffis, a writer who travels around the world as she works, and Luna, her sprightly 4-year-old Schnauzer-Yorkie mix, are nearly inseparable. They have dined in Mexican cafes near Puerto Vallarta, navigated the Paris Metro and hiked the alpine foothills of the Matterhorn.

They rarely go anywhere apart — even on airplanes.

Luna is certified as an emotional support animal, a designation under federal law that allows her — if so desired — to sit on her companion’s lap, instead of being in a cage under a seat, where regular pets must ride. And at a time when airlines are flying at near capacity and charging for seemingly everything but peanuts, Luna rides free.

Classifying animals as emotional support animals has long been permitted under antidiscrimination laws, allowing owners to take them into restaurants and shops or to residential buildings that have no-pet policies. To demonstrate the need for an emotional support animal, the animal’s owner needs a letter from a mental health professional.

But their presence on airplanes is increasingly facing a backlash from flight attendants, passengers with allergies and owners of service animals, like Seeing Eye dogs, who say that airplane cabins have become crowded with uncaged animals who have no business being there. The Department of Transportation does not require airlines to keep data on emotional support animals. One that does, JetBlue expects more than 20,000 emotional support and service animals this year.