I believe that transporter technology has sometimes been used to transfer fetuses from one womb to another. I don't remember which episode or episodes I might have seen it in, and there are about 800 episodes to choose from.
In Deep Space Nine "Body Parts" the fetus of Kirayoshi O'Brien is transferred from his Mother Keiko to his surrogate mother Kira after Keiko is injured. But the dialog doesn't say how Dr. Bashir did it.
BASHIR: Kira almost had us clear of the asteroid field, and then the deflectors became overwhelmed. We were side-swiped by a rock the size of this room. A fuel pod exploded and Keiko was thrown against the bulkhead. She had a concussion, broken ribs, internal haemorrhaging. I managed to stabilise her but the baby's autonomic functions were failing. I had to find another womb for the baby, and the only two people available were Major Kira and me.
SISKO: I think you made the right choice, Doctor.
O'BRIEN: But the Major's Bajoran. How can she carry a human child?
BASHIR: I had to stimulate Kira's estrogen and progesterone production, and administer high doses of tesokine to enable the baby to metabolise Bajoran nutrients.
SISKO: But the bottom line is it worked, right?
O'BRIEN: So, when will Keiko will be strong enough to take the baby back?
BASHIR: Well, Keiko should be up on her feet in a day or two. However, the baby
BASHIR: Major Kira will have to carry the baby to term. You see, Chief, Bajoran women carry their children for less than five months. Because they have such a short gestation period, they vascularise very quickly. Mother and child form a complex interconnecting network of blood vessels. In order to transfer the baby back to Keiko, I would have to sever those ties, which would likely cause massive internal haemorrhage in Kira and a severe respiratory trauma for the baby.
O'BRIEN: So, what you're telling me is that Major Kira's going to have my baby?
This doesn't actually say that Dr. Bashir used a transporter to move Kirayoshi from one womb to another, but the way he adjusted the body chemistry so that a woman could bear a child of another species seems like very advanced medicine.