From The Telegraph:

Just 3/4 of an inch high, the stamp-sized pair is expected to fetch up to £80,000 when sold at Bonhams in London on November 25.

Elizabeth I often commissioned miniatures as personal gifts but Camilla Lombardi of Bonhams said it was likely these were made to mark the end of the affair.

She said: “They can be dated to 1575, a pivotal year in their relationship.

“It is the year when Robert Dudley finally gave up his hope of marrying Queen Elizabeth I.”
…
Both Elizabeth I and the Earl of Leicester were patrons of the artist, Nicholas Hilliard, described by Lombardi as “the father of miniatures”.

They were painted using watercolours on vellum, the skin of an unborn animal, and would originally have formed part of a piece of jewellery.

Bonhams described them as “a remarkable survivor from the Tudor period”.

Full article

Press release from the auction house about the miniatures.

Bonhams website

Boy do I wish I had about £80,000 to spare…

Update:
Here’s an article about the sale. As Marilyn noted in the comments, the final price was £72,000. To me it seems like a good price for two Hilliard miniatures, especially a pair like this.