Mr. Olp said his firm is likely to also join any appeal of recent cases in Chicago and San Francisco, involving women who froze embryos when they received cancer diagnoses and sought to use them after treatment, over the fathers’ objections.

The cases are part of the broader “personhood” debate that has become central to abortion politics. Advocates in many states are seeking laws that would make embryos full legal persons at fertilization — blocking not only abortion but also some forms of contraception and assisted reproduction. None have passed, and some anti-abortion groups say such laws go too far. But some Republican presidential candidates — Senators Ted Cruz and Rand Paul, and Mike Huckabee — support the personhood approach.

Anti-abortion groups turned their attention to custody of frozen embryos only recently. “Traditionally, even though excess embryos were produced, in vitro fertilization was seen as helping people have babies, so there was little interaction between that and anti-abortion advocacy,” said Lisa Ikemoto, a professor at the University of California, Davis, School of Law. “But as the debate over human embryonic stem-cell research heated up, anti-abortion groups woke up to the frozen embryo issue.”

Over the last decade, advocates seeking to represent embryos that might be killed in stem-cell research have challenged funding for such research, according to Judith F. Daar, a professor at Whittier Law School, but the courts rejected the cases, saying they had no standing to sue on behalf of such an amorphous group of embryos.

“These new cases are different in that they deal with specific identifiable embryos,” she said. “And the outside groups here are not trying to represent the embryos, but rather to make a case that the standard used should be the best interest of the embryo.”

The embryo disputes somewhat echo well-known right-to-die cases in which anti-abortion groups fought the removal of life support from patients in vegetative states — among them, Karen Ann Quinlan, Terri Schiavo and Nancy Cruzan.