Sandon, who was the resident expert on porcelain and pottery on the BBC series, died “peacefully” on Monday, according to his family.
His son, John Sandon, also became a porcelain expert on Antiques Roadshow.
In a statement to the PA news agency, John Sandon said: “My dad died peacefully on Christmas morning. Simply old age, as he was 95, and he’s left the world of antiques with an incredible legacy.
“On the Antiques Roadshow chatting to the owner of the most humble cracked teapot, his enthusiasm and his infectious laugh and smile brought their treasured pot to life.
“Dad taught me to see the human side of a piece of pottery, and I could have asked for no greater gift.”
Henry Sandon was known for his knowledge of Worcester porcelain and was a curator of the Dyson Perrins Museum, which became the Worcester Porcelain Museum and then the Museum of Royal Worcester.
He also was a patron of the museum.
The museum wrote in a post on X, formerly Twitter, on Tuesday: “It is with great sadness we share the news that Henry Sandon passed away on Christmas morning.
“Our curator and then patron of the Museum for many years, a much-loved expert who shared his knowledge and enthusiasm for pots and Worcester in person, in books & on tv. Sorely missed.”
In the 1990s, Henry Sandon, who first joined Antiques Roadshow in 1979, memorably found Ozzie the Owl during an episode.
The slipware owl that was brought along to the roadshow in Northampton, where Sandon gave it a valuation of £20,000.
John Sandon also discovered a rare, 17th-century slipware cup during an episode in 2004 which had been bought for £500. He gave it an estimated value of £50,000.
Henry Sandon became a MBE for services to broadcasting, the ceramics industry and charity in 2008.