As ever-more-massive container ships are launched onto the world’s oceans, experts say the risks associated with the vessels could test the capacity of ports and insurers to cope with them.

The rise of so-called megaships has been welcomed by shipping companies but is raising concerns in the insurance sector about the potential for major losses in the event of an accident.

Shipowners and operators, meanwhile, maintain the vessels are safe, economical and environmentally sound.

What exactly constitutes a megaship is open to some discussion as the vessels continue to increase in size.

Stephen Harris, senior vice president of Marsh Ltd.’s global marine practice in Norwich, England, said that over a decade ago, when Copenhagen-based A.P. Moller-Maersk Group took delivery of its first E-class of container ship, which could carry about 15,000 boxes, “we thought that’s it, they’re not going to get any bigger.” E-class is terminology used specifically by Maersk to grade its vessels.

“How wrong we were,” Mr. Harris said. “It became a contest, it seemed, between the major lines almost on a weekly basis as to who was going to order even bigger container ships. When we use the term ‘mega containership’, we take that to mean the ones that started at 18,000 TEU (twenty-foot equivalent unit) — the first of which being the Maersk McKinney Moller that was delivered in 2013 — and of course they’ve just grown and grown from then.”

Last year, according to published reports, CMA CGM S.A., based in Marseille, France, ordered nine 22,000 TEU container ships, followed a short time later by Geneva-based MSC Mediterranean Shipping Co. S.A., which ordered 11 22,000 TEU container ships.

“It’s a moving target,” said Andrew Kinsey, New York-based senior marine risk consultant for Allianz Global Corporate & Specialty S.E. “The exponential growth of container vessels is really shocking.”

Mr. Kinsey said some ports are conducting dredging projects to accommodate the megaships as the vessels exceed the capacity of ports’ infrastructure.

Mr. Kinsey said insurers have been responding cautiously to the larger vessels.

“When you talk about so many containers on one vessel, the exposure from an insurance point of view, it can literally be a scenario when all their eggs are in one basket,” he said. “What we try to tell insurers is keep it diversified. Just because it’s the new shiny penny doesn’t mean you have to use it ... Is it worth the risk? Is the benefit worth the exposure?”

“A worst-case scenario for the insurance market would be to have one of these vessels sinking, taking a very large amount of high-value cargo with it,” which would hit marine hull and cargo insurers, Mr. Harris said.

In addition, an accident involving a megaship could cause significant pollution which, if released into the environment after an accident, could see the operator incur liabilities that could impact the vessel’s protection and indemnity insurer or club, he said.

“When one considers that the value of a new mega containership can be in excess of $150 million and once the potential value of all the cargo being carried in those thousands of boxes on board is added, which could be much more than the value of the ship, plus all the potential liabilities that could be incurred following a loss or accident are taken into account, there are very few insurance marketplaces in around the world that could cope with that sort of loss on their own,” Mr. Harris said.

As the world economy grows over the next 20 years, “we may see vessels much, much bigger than what we’re talking about now,” he added.

Alan Jervis, president of Jervis Marine Insurance Experts International in Toronto, said finding insurance capacity to insure megaships is always going to be an issue.

“So far, the insurance capacity is there,” he said, “but the bigger the vessels become, the more difficult it’s going to be to have the insurance capacity or reinsurance capacity to insure them, and the greater risk of a catastrophic loss, particularly if two megavessels are involved in a collision.” Lars Henneberg, head of insurance and risk management at Maersk, said in a statement that the company is “aware of the concerns expressed by some parties in this ongoing debate.”

“In recent years, we have had constructive dialogues with ship insurers regarding our new buildings and have in each instance not seen restrictions in availability of insurance,” Mr. Henneberg said.