These days, a medical procedure known as âegg freezing,â also known as âoocyte cryopreservation,â is done to increase a womanâs window of fertility, which involves removing, freezing, and storing her eggs.These days, a medical procedure known as âegg freezing,â also known as âoocyte cryopreservation,â is done to increase a womanâs window of fertility, which involves removing, freezing, and storing her eggs.