Elfstone

The Evenstar

The Evenstar, or Elfstone, is a jewel of remarkable beauty that Arwen gifted to Aragorn in Rivendell. It emits an eerie ringing sound, and glows a pale blue.

In Peter Jackson's Return of the King, the jewel appears to shatter on the floors of Minas Tirith, when Aragorn looks into the Palantir, and shows Sauron the reforged Anduril, Sauron shows him Arwen, nearly dead waiting for Aragorn in Rivindell. Aragorn steps back, dropping the Palantir, and as he moves away, the jewel falls from under his coat and shatters on the floor. The next morning, as Aragorn and co. ride to the Black Gate, Aragorn looks completely unstricken, so this may have been some kind of illusion demonstrating the connection between Arwen and the Evenstar, and the fact she is dying.

However the jewel is not seen again in the film, so it may indeed have been destroyed.