A Kashmir sapphire, the biggest to ever be auctioned, sold for $3.88 million at auction in Geneva.
The 55.19-carat gem was formerly in the collection of Maureen Constance Guinness, a marchioness of the Anglo-Irish brewing family, who died in 1998.
Kashmir sapphires of more than 30 carats are very rare and it was sold alongside one weighing 25.97 carats.
"Kashmir sapphires are among the rarest coloured gemstones known to man," said Benoit Repellin, head of magnificent jewels sales at Sotheby's in Geneva. "These gems have over the years acquired an almost legendary status."
A royal tiara, featuring graduated scroll motifs set with diamonds and natural pearls, sold for $1.66m.
The tiara was a gift to Maria Vittoria dal Pozzo on her marriage in 1867 to Amadeo I of the Italian House of Savoy, later king of Spain, and was passed down through generations of Italy's royal family.
"It's a true, beautiful and historic piece which has remained in the House of Savoy for more than 150 years," Mr Repellin said.
The Sotheby's sale went ahead on Tuesday in the Swiss city, with Christie's due to hold an auction of magnificent jewels there on Wednesday.
Marking the 200th anniversary of Napoleon's death, Christie's is selling nine imperial jewels adorned with sapphires and diamonds from the collection of his adopted daughter Stephanie de Beauharnais.
The pieces include a tiara valued at up to $275,000 and a necklace estimated at $350,000, which has "remained in the same family since they were offered to Stephanie de Beauharnais on her wedding at the Tuileries Palace" in Paris, said Marie-Cecile Cisamolo, a jewellery specialist at Christie's.
A total of 38 sapphires from Sri Lanka were used to create the set in the early 1800s.
Another star of the Christie's show is the Spectacle, a 100.94-carat flawless diamond estimated at $12m to $18m.
It is the largest stone to have been cut in Russia and was hewn from a rough stone unearthed in the remote north-eastern Yakutia region in 2016.
The Christie's sale includes a sapphire crown worn by Queen Mary II of Portugal, who reigned twice before her death in 1853.