The most popular dog in the country for the last two years has been the French bulldog, beloved for its batlike ears and deep wrinkles. But because of their flat faces, they are prone to respiratory and eye problems.

That may be why “Frenchies” are the second-most-expensive dog breed to insure, behind the Cane Corso, a mastiff, according to Spot Pet Insurance, one of dozens of companies selling pet health insurance. The company recently ranked the costliest breeds of dogs and cats to cover, noting that some purebreds may be more expensive because their genetic makeup makes them susceptible to certain health conditions.

The rankings were based on average policy premiums as well as the most costly claim paid for the breed, said Trey Ferro, chief executive of Spot Pet Insurance, which has 330,000 active policies. (The dog’s age and the type of policy chosen can also affect costs, the company said.)

At the other end, the cheapest breeds to insure were the Chihuahua and the Maltipoo, a Maltese-poodle cross.

Dr. Jerry Klein, chief veterinary officer for the American Kennel Club, noted that a majority of dog breeds on the insurer’s most-costly-to-cover list — the compact Frenchie aside — were larger animals, while small breeds dominated the least-costly list.

“Big dogs cost more, period,” Dr. Klein said. They eat more, they need bigger crates and other equipment, and if they need medical care, they require larger doses of medicine and anesthesia, he said.

Regardless of breed, Dr. Klein said, “every dog can get sick.” Mixed-breed dogs are less disposed to genetic maladies, according to the North American Pet Health Insurance Association, a trade group whose three dozen members insure the majority of covered pets. But they can still be injured in accidents or dogfights, or develop illnesses.

Among the most common canine ailments resulting in claims are gastrointestinal upsets like diarrhea and vomiting, skin conditions, urinary tract infections, ear infections and allergies, the insurance association said.

And the cost of treatment is going up. The Consumer Price Index was up 3.4 percent overall in April from a year earlier, while the veterinarian services category rose 7.1 percent, according to the Bureau of Labor Statistics. Contributing to the surge in veterinary costs are a tight supply of veterinarians and technicians, more sophisticated medicine and treatments and increased investor ownership of veterinary practices.

The most expensive pet claim paid in 2023, according to the pet health insurance association, was $51,133 for a golden retriever with lymphoma. Other top claims included $46,900 for a vomiting black and tan coonhound, and $43,389 to treat a French bulldog with a corneal ulcer.

Mr. Ferro said his own German shepherd had died about six months ago from liver cancer, leading to a $12,000 bill for three months of chemotherapy. (His insurance policy covered all but $2,000.) And when a Labrador retriever owned by another company officer gulped down a bagel impaled with a toothpick, he said, most of the resulting $10,5000 surgical bill was covered as well.

Such bills make clear why more pet owners are interested in insurance. About 5.7 million pets were insured in the United States in 2023, the pet health insurance association reported, up from 4.8 million in 2022.

While people have always had strong bonds with their pets, they grew even stronger during the pandemic as people stayed home all day, said Kristen Lynch, the association’s executive director. Many pet owners let their dogs sleep in their beds, and half of American owners consider their pets — especially dogs — as much a part of their family as human relatives, a Pew Research Center survey found.

“In our lifetime, we have gone from the barnyard to the backyard to the bedroom,” Ms. Lynch said, so people are loath to face a situation where they can’t pay for lifesaving treatment for a pet.

Choosing pet coverage, however, can be challenging because rates vary not only by breed but also by the pet’s age and location and the type of policy, said Brian Vines, deputy editor for special projects at Consumer Reports, who recently analyzed pet policies. Pet insurance policies have many options and can be customized, he said, but that makes it difficult to compare them because “there’s so much variability.” Deductibles and co-payments can mean substantial bills even with insurance, Mr. Vines said.

His advice is to call around and get quotes from multiple insurers for your specific requirements. “You really have to do the legwork,” he said.

Despite incidents when staggering bills were covered, he said, a survey of about 2,000 Consumer Reports readers with pet insurance suggested that “most folks break even, at best.”

The average monthly health insurance premium in 2023 was about $56 for accident and illness coverage for a dog and about $32 for a cat, the insurance association said. Such policies cover injury from ingesting things they shouldn’t, cuts, car accidents, ligament tears and poisoning, as well as treatments for cancer, infections and digestive problems. Some add wellness coverage, like routine vaccinations and dental care, at an extra cost.

And what about cats?

The costliest felines to insure were the Maine coon, one of the largest house cats, which can be prone to a type of muscle atrophy, and the chinchilla, a popular longhair, Spot Pet Insurance said. The least expensive were the Russian blue and the Siamese.

Here are some questions and answers about pet health costs:

How does pet health insurance work?

In general, you choose the vet you want and pay the bill upfront, then file with the insurer for reimbursement. (Most companies process claims within a day or two, although complex claims can take as long as two weeks, the pet health insurance association says.) Policies usually have a waiting period, from a day or two to as long as 30 days, before coverage starts. Policies usually do not cover pre-existing conditions. As pets age, they generally require more care, so your premium and deductibles will typically increase over time. Some insurers won’t offer new coverage to pets past a certain age. Some policies may offer discounts for covering multiple pets.

How can I reduce the risk of acquiring a dog with serious health ailments?

Dr. Klein at the American Kennel Club advised researching breed characteristics and seeking a reputable breeder, such as one recognized by the club as a “breeder of merit,” meaning the breeder meets criteria like performing health screens recommended for the breed. A directory of individual breed clubs, which can provide referrals, is available on the kennel club’s website. Another resource he suggested is the Orthopedic Foundation for Animals, a nonprofit in Columbia, Mo., that works with breeders to encourage screening for genetic diseases, such as canine hip dysplasia, a degenerative disorder causing loose joints and arthritis.

What if I can’t afford vet bills or pet health insurance?

Mr. Vines suggests calling around to local vets to check prices for services, since they can vary widely. Some practices may allow you to pay over time or have funds set aside to help cover care when owners can’t afford it. So ask your vet. Also, pet telehealth services may be less expensive than in-person visits. Try setting aside money in a savings account to cover needed care. The Humane Society offers a Pet Help Finder tool on its website to find “financially friendly” vets in your area. Local shelters and animal rescue organizations may also offer help or referrals.