[narfforc]

I think the artifact you are looking for was The Elessar. It was a green jewel which had healing power, this jewel was made in Gondolin and given to Turgons daughter Idril, she in turn gave it to Earendil. The Elessar that Arwen gave to Aragorn, could have been this jewel, brought out of Aman or it was another jewel altogether.

There was also The Elendilmir, which was a white star of elvish crystal upon a fillet of mithril, that was lost when Isildur fell into the Anduin. Another jewel of the same name was crafted for Valandil in Imladris, and was worn by the Kings of Arnor upon the brow. The first Elendilmir was found after Saruman had vacated Orthanc, and so Aragorn was in posession of the two Elendilmirs and The Elessar. The film has confused these jewels and created a hybrid, or is Arwen (film) supposed to be returning a family heirloom to the descendant of the Kings of Arnor?

Another artifact in the posession of Aragorn was the Ring of Barahir, the same ring Beren held to prove his ancestry to Finrod Felagund.