Much could be done to shore up old buildings, but that is invariably expensive — and most park services and heritage agencies are badly underfunded. Beyond money, the agencies face deep philosophical issues. How far will they ultimately be willing to go to salvage buildings or parks at risk? Should they, for instance, build sea walls that would forever alter the character of old forts or other coastal sites?

In Tasmania, the archaeology manager of the Port Arthur Historic Site Management Authority, David Roe, wrestles with such questions. The historic site has spent $5 million reinforcing old prison buildings, which are under attack by the rising salt water in the soil and also vulnerable to wind damage. But Dr. Roe is reluctant to consider more aggressive solutions, like a sea wall that would isolate the site from the ocean that connected it to a once-mighty empire.

As he sees the matter, to build such a thing would be to undermine the cultural value that made the place worth preserving.

“We can’t retreat” from the rising sea, Dr. Roe said. “We can’t elevate. We can’t rebuild. Perhaps all we can do is manage loss.”

David Luchsinger was in charge of the Statue of Liberty for the National Park Service when Hurricane Sandy ravaged Liberty Island in 2012, and he led the team that brought the park back to life on July 4 the following year. Mr. Luchsinger, retired and living in New Hampshire, said the issue with historic sites was not just finding the money to make them more resilient, but also slowing the emissions that are putting them at risk in the first place.

“To turn a blind eye on how sea-level rise and climate change are going to affect preserving our history is just, to me, unacceptable,” he said. “That’s where we come from. That is who we are.”