The US president asked the SNP leader to stand up during the ceremony at Trump International Golf Links, saying: “John Swinney is a terrific guy – and loves golf and loves the people of this country, and we really appreciate it.
“You’re really a very special guy. Thank you very much for everything, John.”
Mr Trump’s private visit to Scotland is coming to an end, with the president due to fly back on Air Force One to Washington DC later on Tuesday.
His holiday has included a trip to Trump Turnberry in South Ayrshire and meetings with Prime Minister Sir Keir Starmer, EU chief Ursula von der Leyen, and Mr Swinney.
The first minister later said the president showed a “willingness” to move on the 10% tariff on Scotch whisky.
Mr Swinney said: “I think there is an opportunity for us to make progress.
“I wouldn’t have expected to be able to get an outcome in the course of the discussion I had yesterday and this morning with President Trump, but we will follow this up with the US administration, follow up with the United Kingdom government, to make the progress that I think Scotland would expect on this matter.”
Protests have taken place in opposition against Mr Trump’s visit, but the president appears to have been mostly left in peace to enjoy several rounds of golf.
Mr Trump arrived to the sound of bagpipes and was joined by sons Eric and Donald Jnr as he cut the red ribbon in front of special guests in celebration of the New Course opening.
The president praised Eric’s hard work in the development of the project in Menie, adding: “We started with a beautiful piece of land, but we made it much more beautiful.
“The area has really welcomed us. If you remember at the beginning there wasn’t quite a welcome, but it wasn’t bad. But with time they liked us more and more, now they love us and we love them.”
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Mr Trump said he was looking forward to playing the course ahead of his return to the US.
He said: “We’ll play it very quickly and then I go back to DC and we put out fires all over the world. We did one yesterday – you know, we stopped a war. We’ve stopped about five wars.
“That’s much more important than playing golf. As much as I like it, it’s much more important.”
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Mr Trump also referred to late James Bond star Sean Connery’s reported support for his golf resort.
The president said: “This has been an unbelievable development. The land, they said it couldn’t get zoned, it was an impossibility.
“And Sean Connery said, ‘Let the bloody bloke build his golf course’. Once he said that everything came into line. John and I were talking about that last night.”
Construction of the New Course began in 2023, with Trump International Scotland branding the two courses as the “greatest 36 holes in golf”.
Critics have argued the Trump developments in Scotland have not delivered as many jobs as promised and work at the Menie site has caused environmental damage.
Mr Trump said: “It’s going to be a special day, and it’s going to be a special year, and it’s going to be a special decade.
“And we’re going to make all of our countries strong and great and really wonderful again – and that’s happening and it’s happening very fast.
“And we love Scotland. You know, my mother was born here, and she loved it.
“She would come back here religiously once a year during the summers with my sister Maryanne and sometimes my sister Elizabeth.”
The president said his family would visit Stornoway on the Isle of Lewis.
Mr Trump added: “That’s serious Scotland by the way, there’s no doubt about that.”