The failure of systems used to store frozen eggs and embryos at two fertility clinics has rattled people who count on such clinics to help them realize their hopes of having children. But the breakdowns at clinics in Cleveland and San Francisco, each apparently involving the temperature or level of liquid nitrogen in one storage tank, have damaged at least some eggs and embryos belonging to potentially hundreds of people.

At a time when egg freezing is increasing swiftly — some Silicon Valley companies now tout it as a perk for their employees — the incidents raise questions about what to look for and ask if you are considering taking that step. Here is a basic guide:

How likely are storage failures?

Several doctors with years of experience in the fertility industry say the recent incidents in San Francisco and Cleveland appear to be unusual. “I’m not aware of any other instances,” said Catherine Racowsky, the director of the IVF lab at Brigham and Women’s Hospital in Boston, who has served on several professional and government oversight committees.

Dr. Racowsky and others said that fertility clinics — there are about 450 to 500 in the United States — tend to have backup systems to handle technical failures and make sure frozen tissue stays frozen. “It’s every clinic’s nightmare,” said Dr. Julie Lamb, director of fertility preservation at Pacific NW Fertility in Seattle. She has been fielding questions this week from concerned patients, assuring them that the clinic has multiple backup storage tanks, freezers checked by staff members twice daily, and a “specialized alarm system that monitors tanks, monitors the temperature in the nitrogen level and is connected to a whole phone system with multiple layers of alarms.”

Jake Anderson, a founder of Fertility IQ, a website that provides assessments of fertility doctors and clinics, noted that both the Cleveland and San Francisco clinics are “large, reputable, subject to oversight,” and they both quickly acknowledged the failures publicly. But he said he worried about smaller, private clinics that have no affiliation with a university or hospital and whether some would be less inclined to disclose a problem. “If this happens in other places that are private, people would take this to the grave and they would never breathe a word of this,” Mr. Anderson said. “To think that only the well-run places that have boards and clinical oversight — they’re the only ones having this problem? I believe the opposite.”