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This story is part of an occasional series, "Making Babies: 21st Century Families."

As more women postpone motherhood into their 30s, even 40s, they're hitting that age-old constraint: the biological clock. Now, technology is dangling the possibility that women can stop that clock, at least for a while.

In a Manhattan office building on a recent evening, two dozen women — all in their 30s and 40s — sit in folding chairs, balancing cellphones and glasses of wine. They're gathered for a seminar called "Take Control of Your Fertility."

Dr. Alan Copperman of Reproductive Medicine Associates of New York wastes no time laying out this harsh reality: By the time a woman hits her 40s, 90 percent of her eggs are abnormal. The chances of a typical 40-year-old getting pregnant in any given month? Ten percent. Unless, that is, she gets pregnant with her younger eggs — eggs she had frozen years before.

Copperman explains the procedure, introduces someone who has gone through it and takes a flurry of questions.

Afterward, women crowd a counter to set up appointments...