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.

“It’s becoming a big problem,” said Marcie Davis, founder of International Assistance Dog Week. “I’ve seen people bring on pets and try to pass them off as an emotional support or service dog. It’s not appropriate and it’s not safe.” [...]

“Assistance dogs are trained not to bark in public, not to go smelling other dogs or people,” she said. “I’ve had my dog attacked in multiple situations. Honestly, I understand that there’s some value that people need an emotional assistance dog. But I think a lot of this is that people love their dogs and think they feel like if you have your dog, why can’t I have mine?”

To serve the needs of the animals and their owners, a cottage industry of websites and doctors advertising documents that certify emotional support animals has emerged.

Carla Black, a psychotherapist in Marina del Rey, Calif., began receiving enough requests for emotional support animal certification that this year she began advertising on her website. For $99, she provides an hour of her time, over the phone or Skype, and a clinical assessment, along with a prescription letter, which is valid for one year.