Along with a copy of the US Declaration of Independence and a mezzotint of George III, the last American monarch, Trump was shown pictures of the queen's father, George VI, and her uncle Edward VIII playing golf in Scotland.
There was also a letter from George VI to his father George V, saying he had beaten his brother.
Trump, who owns two golf Scottish courses, asked questions and smiled as Elizabeth explained the provenance of items, appearing to take particular interest in the golfing items.
Among other historical artifacts, Elizabeth showed the Trumps a portrait of George Washington, the first president of the United States, and a draft copy of a telegram from George VI to US General Dwight Eisenhower after the D-Day invasion of France.
Prince Charles and his wife Camilla also attended the viewing, as did Ivanka Trump and her husband, Jared Kushner.
Charles's second son, Prince Harry, husband of former US actress Meghan Markle, and the queen's second son, Prince Andrew, were also present for the tour.