“The unique thing about IUDs and implants is that they last for so long,” said Dr. Lydia Pace, an assistant professor of medicine at Harvard Medical School and the lead author of the study. Because the devices were so long-lasting, women were taking advantage of insurance coverage provided under the Affordable Care Act, and getting a birth control method with the longevity to weather potential policy changes.

The IUD, a small device placed in the uterus, has been shown to be more than 99 percent effective at preventing pregnancy and can work for up to 12 years, depending on the type. But without insurance coverage, IUDs can be expensive: Out-of-pocket costs can be from $500 to $1,000. Implants are also more than 99 percent effective and last up to five years, but can cost up to $1,300 without insurance.

The study, which only looked at women enrolled in commercial health insurance, found a 21.6 percent increase in the insertion rates of long-acting reversible contraceptive methods among women ages 18-45 in the 30 days after Mr. Trump was elected.

When the researchers examined the 30 days before and after the election, and compared it to the same time period in 2015, they found that an additional 2.1 IUDs or implants inserted per 100,000 women per day were associated with the election, though it isn’t possible to know for sure because they did not study the motivation of the women who received them. If these results were extrapolated to the 33 million women in the United States between the ages of 18 to 45 who have employer-sponsored health insurance, it would mean that an estimated 21,000 additional devices and implants were inserted in the month after the election, Dr. Pace said, an increase she described as “impressive.”

“Was there something else that happened that could account for that rise?” Dr. Pace asked. “Not that I know of.”