Maybe it was the bonnets.

Or the gloves that the two women donned, though the temperatures in Orlando, Fla., on Wednesday hovered in the 60s.

In a scene right out of a sitcom, the women went to a coronavirus vaccination site “dressed up as grannies,” said Dr. Raul Pino, the health administrator for Orange County, at a news conference on Thursday. Except they were 34 and 44, not over 65, so despite their get-ups, which included spectacles, they were ineligible to get the shots in Florida.

However, the ruse may have worked before. The women presented valid Centers for Disease Control and Prevention cards indicating that they had already received their first vaccine doses, Dr. Pino said, who did not name them. “I don’t know how they escaped the first time,” he said.

Florida has vaccinated about 42 percent of its more than 4.4 million people 65 and older, according to the state, and health care workers and people with some underlying conditions are also eligible for the shots. It is unclear when the administration of Gov. Ron DeSantis, a Republican, will consider that enough of those populations have been vaccinated to open eligibility more widely.

The state is one of many where vaccines are in high demand because of a lag in shipments from weather delays.

Younger people, teachers, police officers and other essential workers are all clamoring for doses, but Florida has not said which group it will prioritize next.

Agencies administering the shots have had to be “very careful” about people “faking it,” Dr. Pino said. “It’s probably higher than we suspect,” he said, adding that at least one man who was too young for a shot tried to pass himself off as his father, who had the same name.

“Our job as a health department is to vaccinate as many people as possible, as fast as possible,” Dr. Pino said, adding that the state’s Department of Health was following the governor’s priorities, which are based on modified C.D.C. guidelines.

On Wednesday, Health Department staff asked sheriff’s deputies to issue trespass warnings to the bonnet-clad women, whose birth dates did not match those that they had used to register for the vaccines, a spokesperson for the sheriff’s office said.

They were not charged with any wrongdoing. But they did not receive the vaccine.