NEW YORK — The private treasures of Frank Sinatra and his wife, Barbara, were a multimillion-dollar hit at auction.

Sotheby’s reported Friday that the couple’s entertainment memorabilia, art, jewelry, books and other personal items sold for $9.2 million — about twice their pre-sale estimates.

Nine paintings by the legendary crooner went for more than $850,000, against a high estimate of $120,000.

The 20-carat diamond engagement ring Sinatra presented to his fiancee in a glass of champagne fetched nearly $1.7 million, surpassing a top $1.5 million estimate.

And a Jewish skullcap with Frank’s name embroidered on it shot past a high estimate of $500, selling for more than $9,000.

Some of the proceeds will benefit the Barbara Sinatra Children’s Center in Rancho Mirage, California, which counsels victims of physical, sexual and emotional abuse.