Mrs. Trump was not the star of this first trip; that role could be played only by Mr. Trump. But she was one of its most intriguing figures, at times sphinx-like, at times expressive, and always fashionable, with a glamorous wardrobe that rotated between Michael Kors and Dolce & Gabbana. She was the supporting player who occasionally stole the spotlight.

“Historically, first ladies have made a difference on a trip like this,” said Michael Beschloss, the presidential historian.

Kennedy, he noted, worried that Jacqueline would be a political liability because Americans would view her as elitist. But she was a sensation in France in 1961, charming Charles de Gaulle with her grasp of the French language and the country’s history. She helped smooth the relationship between de Gaulle and Kennedy, and later, between Kennedy and the Soviet leader, Nikita Khrushchev. In doing so, she became a cult figure in the United States.

Given that Mrs. Trump has been a spectral presence in her husband’s White House — mostly staying in New York City with the couple’s son, Barron — this trip was a coming-out party for her. It may also offer a clue as to what kind of first lady she is likely to become: neither the independent-minded equal partner that Hillary Clinton was to Bill Clinton, nor the devoted, long-suffering spouse that Patricia Nixon was to Richard M. Nixon.

By the end of the trip, Mr. Trump seemed to recognize her subdued star power. Speaking to American service members at the Sigonella naval air station in Sicily, he said the United States could not have a better emissary than “our magnificent and wonderful person, our first lady, Melania.”