Ellen Pompeo revealed when her baby daughter Sienna was born, and discussed the top-secret surrogacy process with Jimmy Kimmel on Thursday, Oct. 2. Credit: Donato Sardella/Getty Images

A doctor's discretion! Ellen Pompeo appeared on Jimmy Kimmel Live Thursday, Oct. 2, where she discussed her newborn daughter Sienna May, and the top-secret surrogacy process.

"She was born two months ago," Pompeo, 44, told Kimmel of her baby girl. "I've done it before. The covert thing is kind of fun. This baby was born via surrogate, so I felt an obligation to keep the surrogate's privacy. That was of utmost importance to me."

Pompeo confirmed earlier in the afternoon that she had secretly welcomed her second child with husband Chris Ivery. "Sienna May Ivery welcome to the world," Pompeo wrote on Instagram, alongside an adorable snap of Ivery kissing 5-year-old Stella Luna's younger sister. "We love you more than words can say." The Grey's Anatomy star also gave a sneak peek into her baby Sienna's nursery on Thursday, as seen in the November 2014 issue of Architectural Digest.

Kimmel, though, was most curious about the surrogacy process. "Pardon my ignorance on this," he said to Pompeo. "When you have the baby through a surrogate, does your husband, uh, visit her in the motel room?"

Laughing, the ABC actress responded: "No, no." Stumbling for words, she explained how it worked. "I was present for the insemination. I held her hand. So they take the sperm... medically, Chris Ivery has to do what he has to do, and provide what he has to provide."

She continued, "I had to provide something as well… You have to retrieve the egg. And then they put it together in a dish — the lab technicians — and then they make the embryo. Then they insert the embryo into the woman who will carry the child."

Getting sentimental, Pompeo reflected of her surrogate: "This is an incredible thing to do with your life, to give the gift of carrying someone's child. I am forever grateful and feel very blessed and grateful to her — she who will remain anonymous. I was there with her when they inseminated her, and we held hands. I looked into the microscope and I saw the embryo. I saw the baby, and they put it in a thingy and they inseminated her. And then we held hands and we prayed, we talked to God, and if she was meant to be. He said he was going to try to help us out and now we have a gorgeous baby girl."