Among older women who are unmarried, ages 35 to 39, however, the birthrate was 48 percent higher in 2012 than in 2002, according to the National Center for Health Statistics. The increase was driven by college-educated women, according to Mr. Cohen’s analysis. “The delay in general fits a long-term pattern: that family formation is increasingly delayed until women are more established, spend more time in education and more time developing their careers,” he said.

Over all, older, highly educated women are more likely to have children than they were two decades ago, according to a Pew Research Center report published Thursday.

Many women who chose to have babies on their own after 35 used sperm donors. In interviews, some said they had not yet found a partner before the age when fertility plummets. “I was 40 and dating and dating and dating and just not having any luck,” said Jennifer Williams, now 43, a gerontologist in Pleasant Hill, Calif. She found a sperm donor and went through six rounds of attempts to get pregnant.

Her daughter, Maya, is four months old. “It’s absolutely the best thing I ever did,” she said.

Lizzie Skurnick, 41, a publisher of young adult fiction and a writer, wanted to become a mother, but didn’t want a partner at the time. She used donor sperm to conceive her son Javier, 1, and is considering having another baby in the same way. “If I had married any of the men I had dated, and they are lovely men, I would be carrying them also, because they always made less than I did,” she said. “Honestly, that’s just an additional stress on a household.”

Older women who chose to become single mothers said their decisions brought challenges. Some worried about the financial stress of raising a child on one income. Others feared that their children would miss having a father or a bigger family. Dating is expensive because of the added cost of a babysitter. “The most challenging thing is not having company at the end of the day after she goes to bed,” Ms. Williams said.

For Ms. Skurnick, “the one problem is it’s freaking hard on your back.”

But the benefits, they said, far outweighed the challenges. They avoided spousal arguments over child rearing, which they had seen tear apart friends’ marriages. They had autonomy in making parenting decisions. And by being older, they said, they had more stability. “I feel like I’ve had more life experience to be able to see we’re going to get through rough patches,” Ms. Williams said. Her career was established enough that she could start consulting after she decided she wanted a longer maternity leave than her job provided.

Many policy makers and researchers have shifted their focus from reducing the number of single mothers to bringing down the number of unintended pregnancies, which are riskier for both mothers and babies. Fifty-seven percent of out-of-wedlock pregnancies are unplanned — unchanged from 2002.