The actor was one of the guests at a special reception in New York and was introduced to the Duke and Duchess of Cambridge.
Both Stewart and his wife, singer Sunny Ozell, were at the Creativity is Great reception to celebrate British talent in the United States.
The Duchess and Prince William were on a four-day trip to the States which included a poignant visit to the memorial to the World Trade Centre bombing horror.
Click below for pictures from their visit
The guests at the talent reception included Glenda Bailey, editor-in-chief of Harper’s Bazaar, Amanda berry, chief executive of Bafta, the British Academy of Film and Television Arts, media mogul Harvey Weinstein, and his Marchesa designer wife Georgina Chapman, and author Imogen Lloyd-Webber, daughter of the musicals composer Lord Lloyd-Webber.
As they mingled, the throng dined on British themed canapes including mini Yorkshire puddings and Scotch egg bites washed down with PG Tips tea and Old Speckled Hen ale.
Sir Patrick, who is Chancellor of the University of Huddersfield, said afterwards: "I have met many members of the Royal family before but what a personable, pleasant and, may I say, attractive couple.
"Prince William told me he had never been to New York before which, I must say, surprised me greatly. I was even more surprised that the Duchess hasn’t been. I urged them to come back again incognito. New York is the type of city that turns a blind eye and would allow you to do that."
Sir Patrick said he had recently taken William’s cousin, Princess Eugenie, who is currently working in New York, as his guest to his latest show on Broadway, Waiting for Godot.