Star of Elendil

The Star of Elendil was a white precious jewel (diamond?) worn by Elendil and his heirs, and then by the chieftains of the Dúnedain in Arnor.

The Stars of Elendil were also called the Elendilmir, the Star of the North, and the Star of the North Kingdom.

The jewel was given by Silmariën to Elendil, but probably was not a new creation and existed long before the end of Second Age.

It was lost somewhere in the period surrounding the fall of Arnor, possibly as early as when Isildur was slain. The kings and chieftains of the North then wore an new gem, with the same names.

The original was rediscovered by Saruman's agents while searching for the One Ring, and Aragorn later recovered it from amongst Saruman's treasure in Isengard after the War of the Ring.

It is speculated that the jewel contained, like the Phial of Galadriel, a tiny measure of the light of the Two Trees that once shone in the Silmarils.

Note
In Foster's The Complete Guide to Middle-Earth the Elendilmir is mistakenly identified with the Star of the Dúnedain which was given to Samwise Gamgee, but this is clearly an error.