“By God’s grace, there was never a moment where we thought we were going to have another baby of our own,” Carolyn Savage said.

The doctor told them they could abort, but the couple didn’t consider that a viable option.

“It wasn’t even something we had to discuss,” said Sean Savage, 39.

The Savages won’t reveal the name of the fertility clinic, saying only that it’s not in Ohio. They have hired attorneys who say they are working to make sure the clinic will accept full responsibility.

A message was left Wednesday for the Savages’ Detroit attorney, Brian McKeen.

The Morells, who live north of Detroit, learned of the mistake a day after the Savages. They were just about to start the proce...

“By God’s grace, there was never a moment where we thought we were going to have another baby of our own,” Carolyn Savage said.

The doctor told them they could abort, but the couple didn’t consider that a viable option.

“It wasn’t even something we had to discuss,” said Sean Savage, 39.

The Savages won’t reveal the name of the fertility clinic, saying only that it’s not in Ohio. They have hired attorneys who say they are working to make sure the clinic will accept full responsibility.

A message was left Wednesday for the Savages’ Detroit attorney, Brian McKeen.

The Morells, who live north of Detroit, learned of the mistake a day after the Savages. They were just about to start the process of having another baby with their last embryos when the clinic called.

The two couples knew nothing about each other. Shannon Morell feared that the pregnant woman would choose abortion, ending their chance to give their 2-year-old twin girls a sibling.

“I didn’t think she’d want to carry the baby to term,” Shannon said. “I felt helpless.”

A few days passed before they learned that the Savages were not only willing to continue with the pregnancy, but also to hand over the baby without hesitation.

In the first few weeks, the Savages sent e-mail updates after every doctor’s visit. The couples finally met about three months into the pregnancy.

They shook hands, held back tears and began to form a bond. Phone calls followed.

Then in August, Carolyn Savage asked Shannon Morell whether she wanted to be with her for the ultrasound.

Shannon felt funny, too, being in the same room with Carolyn and her husband. She didn’t want to show too much excitement, knowing how conflicted they must be feeling.

“I felt like the third wheel,” she said. “Although I knew that child inside her was mine, it wasn’t the same feeling I had with the twins.”

The American Society for Reproductive Medicine doesn’t track how many women have been given the wrong embryos, said Eleanor Nicoll, a spokeswoman. Only a few cases have popped up the past decade or so.

Each fertility clinic has its own system for identifying and tracking embryos. M...

Then in August, Carolyn Savage asked Shannon Morell whether she wanted to be with her for the ultrasound.

Shannon felt funny, too, being in the same room with Carolyn and her husband. She didn’t want to show too much excitement, knowing how conflicted they must be feeling.

“I felt like the third wheel,” she said. “Although I knew that child inside her was mine, it wasn’t the same feeling I had with the twins.”

The American Society for Reproductive Medicine doesn’t track how many women have been given the wrong embryos, said Eleanor Nicoll, a spokeswoman. Only a few cases have popped up the past decade or so.

Each fertility clinic has its own system for identifying and tracking embryos. Most patients get an identification number that also is kept with the embryos while they are stored. Names are double-checked. So are the numbers.

The Savages and the Morells say they have not been told what exactly went wrong at their clinic.

Neither family is sure what will happen after the baby is handed over to the Morells. They plan on approaching it like they have so far—with caution and care—making sure not to cause any more pain.

Carolyn Savage won’t have another chance to carry her own baby because of her age and difficulties during her earlier pregnancies. She and her husband plan to hire a surrogate and try again for a fourth child.

The Morells don’t have a name picked out for their son and aren’t likely to make it public.

His mom doesn’t want him to be known as the baby who got switched at the clinic. She wants to tell him about that herself. And she wonders if someday he’ll want to meet the woman who gave birth to him.

Carolyn Savage said she knows she’ll always think about him, and Shannon Morell plans to send the Savages updates as the baby grows.

“We’ll always have a bond,” she said.