At Baylor, eight women have had transplants, including the new mother, in a clinical trial designed to include 10 patients. One recipient is pregnant, and two others — one of whom received her transplant from a deceased donor — are trying to conceive. Four other transplants failed after the surgery, and the organs had to be removed, said Dr. Giuliano Testa, principal investigator of the research project and surgical chief of abdominal transplantation.

“We had a very rough start, and then hit the right path,” Dr. Testa said in a telephone interview. “Who paid for it in a certain way were the first three women. I feel very thankful for their contribution, more so than I can express.”

Both Dr. Johannesson and Dr. Testa said that a large part of their motivation came from meeting patients and coming to understand how devastated they were to find out that they would not be able to have children.

Dr. Testa said: “I think many men will never understand this fully, to understand the desire of these women to be mothers. What moved all of us is to see the mother holding her baby, when she was told, ‘You will never have it.’”

The transplants are now experimental, with much of the cost covered by research funds. But they are expensive, and if they become part of medical practice, will probably cost hundreds of thousands of dollars. It is not clear that insurers will pay, and Dr. Testa acknowledged that many women who want the surgery will not be able to afford it.

Another hospital, the Cleveland Clinic, performed the first uterus transplant in the United States in February 2016, but it failed after two weeks because of an infection that caused life-threatening hemorrhage and required emergency surgery to remove the organ. The clinic halted its program for an extended period, but has restarted it and has patients awaiting transplants, a spokeswoman, Victoria Vinci, said.