For the Sons of Italy Ball, Cinza Zaccardi (Sophia Loren), an Italian socialite on the run from her domineering father and masquerading as a housekeeper, wears the necklace her mother wore when her father proposed. The necklace is a statement piece set in gold and mounted with emeralds and diamonds, which is most likely from Bvlgari since Sophia is a loyal patron of the brand and thus, it features in many of her films.
The necklace is meant to contrast with all the pearl strands and simple gold and silver chains that all the other women at the party are wearing, signifying that she stands out - a literal diamond among the pebbles.
Whether the necklace was a loan to the film production or a part of Sophia's personal collection is not relevant as it is not known where it is currently. If it were personally owned by Sophia, it may have been part of Sophia's cache of stolen jewelry, most of which had been from Bvlgari and worth millions of dollars, from two thefts - the first at the Norwegian Barn in Elstree in 1960 and the second in her suite at the Sherry Netherland Hotel in New York in 1970.