According to the Lexington Herald Leader, The Kentucky Historical Society paid $19,800 for the earrings in 2008.
And how did know they were genuine?

Documents on file at the Historical Society that came with the earrings trace them back to well-known collector Charles F. Gunther of Chicago, who died in 1920. Gunther told the son of the man to whom he sold or traded the earrings that “he knew they were Mrs. Lincoln’s earrings but he couldn’t remember why he knew it,” the son’s daughter wrote in a letter in 1970 to another collector who had purchased the earrings from her family.

So there you have it. They’ve got to be real.

You can read more about it here.