Final answer:
A woman without ovaries would benefit most from IVF with donor eggs, as she cannot produce eggs for fertilization. This process allows the embryo to be implanted into her uterus, enabling her to potentially carry a pregnancy to term if her uterus is viable.
Step-by-step explanation:
If a woman lacks ovaries and hence has no viable eggs, the assisted reproductive technology that would most likely help her and her partner have a baby is in vitro fertilization (IVF) with donor eggs. During the IVF treatment, an egg from a donor and the sperm from the intended father are combined outside the body. This process is followed by implantation of the embryo into the uterus of the woman who lacks ovaries. Since the woman cannot produce her own eggs, ovulation-stimulating drugs would not be effective. Other treatments such as Gamete Intrafallopian Transfer (GIFT) are also not suitable because they require eggs from the woman. Surrogacy could be considered in case the woman also has a nonviable uterus or other health issues that prevent her from carrying a pregnancy to term.