Georgina Shiels, from Kilrea, had an animated exchange with the prince.
Mrs Shiels, who is welfare officer of the Causeway Coast branch of the Royal Air Forces Association, showed the heir to the throne a thank you card that she had received from the royal couple after she had written to congratulate them on their wedding in 2011.
The prince was clearly fascinated at the discovery.
“He said: ‘Wow! Would you like me to sign it?’”
Mrs Shiels, a former nurse, did not get the Duke to sign it because she was worried that she would be breaching the security rules, but she quickly regretted her failure to take the prince up on his offer.
“I wish I’d got him to sign it,” she told the News Letter.
Mrs Shiels was wearing an RAFA badge on her lapel as she talked to Prince William, who is himself an aviator.
Mrs Shiels said she had once met the Queen Mother, who had asked where she was from and when she replied “near Coleraine”, the royal responded: “Oh, I’ve been there.”
She had also met the Queen, the Duke of Edinburgh, Princess Anne, and had waved at Princes Edward and Andrew. Now that she had met the Duke of Cambridge, she said: “The only one I haven’t met is Charles.”