Federal health officials have offered repeated assurances that most American hospitals can safely treat Ebola, but Emory University Hospital in Atlanta, which had years of preparation for just such a crisis, found out how hard that is while it cared for three Ebola patients.

As doctors and nurses there worked to keep desperately ill patients alive in August, the company that hauled medical trash to the incinerator refused to take anything used on an Ebola patient unless it was sterilized first. Couriers would not drive the patients’ blood samples a few blocks away for testing at the Centers for Disease Control and Prevention. And pizza places would not deliver to staff members in any part of the hospital.

“It doesn’t matter how much you plan,” Dr. Bruce Ribner, an infectious disease specialist who directed the patients’ care, said in an interview. “You’re going to be wrong half the time.”

Emory solved its problems, but the challenges it faced could overwhelm a hospital with fewer resources. At Texas Health Presbyterian Hospital in Dallas, mistakes in treating a patient from Liberia — a delay in diagnosing the disease, and its spread to a health worker who had apparently taken all precautions — have raised questions about the general level of preparedness in hospitals around the country. Medical experts have begun to suggest that it might be better to transfer patients to designated centers with special expertise in treating Ebola.