According to Afrojack the 19.88-carat, cushion-shaped, Star of Kashmir Sapphire is the most expensive Kashmir sapphire in the world, having sold for US$ 3,484,102, a world record price, for a whole stone and price-per-carat, ever paid for a blue sapphire. However, I am sorry to say, that Afrojack is probably mistaken, as he might not have been aware of another Christie's Magnificent Sale held in Hong Kong in November 2011, at which another cushion-shaped Kashmir sapphire weighing 26.41 carats and set as the centerpiece of a sapphire and diamond brooch, sold for a whopping US$ 3,838,508 or US$ 145,342 per carat. According to the renowned gemologist Richard W. Wise's blog, - "The GemWise Blog" - the price realized by the 26.41-carat Kashmir sapphire is a new world record for a Kashmir sapphire both for single stone and price-per-carat, pushing the 22.66-carat, Hill's Kashmir Sapphire that held the previous record of US$ 3,064,000 to second place.
The price of US$ 3,484,102 is the second highest price realized for a Kashmir sapphire, and hence the 19.88-carat "Star of Kashmir Sapphire" is actually the second most expensive Kashmir sapphire in the world, followed by the Hill's Kashmir sapphire which occupies the 3rd place and the Rockefeller sapphire occupying the 4th place.
Two images of the 26.41-carat Kashmir sapphire, the current world record holder for the most expensive sapphire, is attached to this post.