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In January, Lynlee Weber testified against a legislative proposal to ban surrogacy contracts. Credit Nick Oxford for The New York Times

When Crystal Kelley, a Connecticut woman who had signed a contract to bear a baby for a couple in her state, was five months pregnant, a routine ultrasound showed that the fetus had a cleft palate, a brain cyst and heart defects. The couple for whom she was carrying the baby asked her to have an abortion, offering to pay her $10,000 to do so.

But instead, Ms. Kelley, a single mother of two, fled to Michigan, where surrogacy contracts are unenforceable. So in June 2012, when she had the baby there, Ms. Kelley was listed on the birth certificate as the mother, although she had no genetic connection to the infant, made with the husband’s sperm and an egg from an anonymous donor. The little girl was adopted by a family that had other special-needs children.

While surrogacy is far more accepted in the United States than in most countries, and increasing rapidly (more than 2,000 babies will be born through it here this year), it remains, like abortion, a polarizing and charged issue. There is nothing resembling a...