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Image of an IVF petri dish

Anna Nibley Baker, a mother of four in Salt Lake City, is reasonably certain that she and her husband are done building their family. Yet for eight years, since the birth of her last child, conceived through in vitro fertilization, she has thought tenderly of the couple’s three remaining embryos, frozen and stored at a university clinic.

Now, after the Supreme Court’s abortion ruling overturning Roe v. Wade, Ms. Baker, 47, like countless infertility patients and their doctors nationwide, has become alarmed that the fate of those embryos may no longer be hers to decide. If states ban abortions starting from conception — and do not distinguish between whether fertilization happens in the womb or in the lab — the implications for routine procedures in infertility treatment could be extraordinary.

In a cycle of I.V.F., a field of medicine that is more than 40 years oldand used by hundreds of thousands of heterosexual and same-sex couples, single people and surrogate carriers in the United States, the hope is to create as many healthy embryos for each patient as...