Star of Elendil
Star of Elendil or Elendilmir was the name given to two noble star-shaped white gems. Both these gems were set on mithril fillets. It was also referred to as Star of the North Kingdom and Star of the North.
The first Elendilmir
The first jewel dated back to the early centuries of Númenor, and belonged to Silmariën, the daughter of King Tar-Elendil. From her, it passed to her descendants the Lords of Andúnië. The last Lord was Elendil, who escaped the Downfall of Númenor and became High King of the Dúnedain in Middle-earth. He wore the Star of Elendil on his brow in place of a crown, as did his son Isildur after him. Isildur had only been King for two years when he was waylaid by Orcs and lost in the Great River.
The second Elendilmir
The original Elendilmir was lost with Isildur, and so a copy was made by the elven smiths of Rivendell for his son Valandil. This second Star of Elendil became the royal symbol of the North-kingdom along with the Sceptre of Annúminas. After that kingdom's fall it remained an heirloom of the Heirs of Isildur. It remained in Isildur's line down to the time of Aragorn, who wore it during the Battle of the Pelennor Fields.
At the time Aragorn became King of Gondor, it was thought that the first Star of Elendil had been lost for more than three thousand years. However, it was later found that, the searchers sent by Saruman (though they had failed in their mission to find the One Ring) had uncovered other things. The original Star of Elendil was discovered in a secret chamber in Saruman's tower of Orthanc.