Garrett Burke designed the quarter dollar, in circulation in California, which features Muir.
Mr Burke made his first visit to East Lothian earlier this month, enjoying a long weekend in Dunbar.
He was impressed with the county's beauty, according to Will Collin, a trustee of the John Muir Birthplace Trust.
Will, who was one of the guides who accompanied Mr Burke on his visit, said: "He and his family were really impressed with East Lothian.
"He really loved the scenery and said how beautiful the county was. He was also touched by the friendliness he was shown by everyone he met here.
"He had never been here before, so there was no doubt it was a great experience for him to come to the birthplace of the person who inspired the design of his quarter dollar coin five years ago.
"I met him at a John Muir conference in California in 2006, and he said that he had been hoping to come over not long after that but his plans fell through. However, once we heard that he was thinking of coming over this year, contact was renewed."
Mr Burke is currently writing a book about the quarter dollars that were produced in 2005 - his one being the 31st in the US Mint's 50-state quarters programme.
His quarter design depicts John Muir, described as the 'Father of Conservation', admiring Yosemite Valley's granite peak, known as the 'Half Dome', and also features a soaring California condor.
The coin bears the inscriptions "California," "John Muir," "Yosemite Valley" and "1850".
As well as being accompanied on a visit of sites relating to John Muir across the county, Mr Burke gave a presentation on his book, which is expected to be published in the near future.
He also helped produce a sand-sculpture of his quarter dollar on the East Beach at Dunbar, as part of the John Muir Birthplace annual sandcastle modelling competition.
Will said that the visit by Mr Burke can only add to the great interest in the work of John Muir and his East Lothian birthplace, especially on the west coast of the United States. "You only have to look at the visitors' book in the museum to see how many people visit here from that part of the world," he said.
"I am sure that this visit can only add to people's fascination with John Muir, his life and work."
Prior to his visit to East Lothian, Mr Burke, his wife Michelle and teenage daughter Katie had been visiting family in Ireland.