As the number of frozen human embryos continues to rise daily, with numbers not expected to fall, an answer must be found to this dilemma. Four possible solutions have been suggested: a) thaw the embryos and allow them to perish; b) thaw them and donate them for biomedical research; c) thaw them and donate them in adoption; and d) leave them frozen indefinitely. This paper will evaluate the morality of these four possible solutions, particularly frozen human embryo adoption in the light of the Magisterium of the Catholic Church, which in its Instruction Dignitas Personae, appears to have opted to consider this practice as illicit. We also review the various stances of expert moralists in favour of or against frozen human embryo adoption, and we reflect on the extent to which the doctrine contained in Dignitas Personae can bind the moral conscience of the Catholic faithful. Finally, we make a personal evaluation of frozen human embryo adoption, in an attempt to find moral reasons that substantiate the negative opinion manifested by the Catholic Magisterium on this matter.