Signs will also be put up and visitors are already warned not to insert the coins by tour guides at the Giant's Causeway, like Mark Adams.
"I think it's a simple thing of wanting to leave something of themselves behind," he said.
"But if you want to leave something behind, take a photo, put it online, it'll be there forever."
Last year, the Giant's Causeway received about 684,000 visits.
The numbers are steadily climbing back to their pre-pandemic levels. There were nearly a million visits in 2019.
The National Trust said not only is it Northern Ireland's most valuable natural phenomenon, it is important for the economy too.
"It's an icon for Northern Ireland - if we can't look after this, what's the hope for the rest of the country?," said Dr Henry.
"We really need to be looking after the causeway as best we can."
The Giant's Causeway became a United Nations Educational, Scientific and Cultural Organisation (UNESCO) World Heritage Site in 1986.
The World Heritage list includes 1,223 properties across the world and recognises the sites for their cultural or natural importance.