Stars were so important to Tolkien's Elves that they are in fact named 'the People of the Stars' -- the Eldar.
First invented by Varda, the Star-Queen, stars were made from the sap of the Silver Tree, Telperion. It is told that the stars were the first things the ancestors of all Elves saw when they awakened on the earth, by the waters of Cuiviénen.
This must have had a huge influence on their fashion. Indeed, as we can see from their heraldic devices drawn by Tolkien, the Noldor loved incorporating stars into their designs. It's not so far out of the realms of imagination that Elves would, then, make and wear jewellery in the form of stars.
Fëanor and his family took as their device the eight-pointed star, which becomes probably the most well-known design in Middle-earth during the First Age, and is still recognised at the end of the Third Age, thousands of years after Fëanor and all his family are gone. It's easy to imagine they might have worn earrings like these Eight-Pointed Star Earrings, or added an Eight-Pointed Star Charm to their bracelets, or maybe even baked their cakes in an Eight-Pointed Star Baking Mold. (They didn't do things by halves.)
Among the constellations of Middle-earth, the Valakirka, the Sickle of the Valar, with its seven stars, was known as a sign of the doom and ultimate defeat of Morgoth. Today we know it as the Big Dipper, but frankly, the Valakirka just sounds about a million times more awesome and I'm totally all about my Valakirka Ear Climber.
The Kings of the Noldor went on to use stars in their heraldic devices for as long as they existed, including their last king, Ereinion Gil-galad, of whom it was sung, "the countless stars of heaven's field/were mirrored in his silver shield." And presumably also in Ereinion Gil-galad's Banner as well.
Even at the end of the Third Age, the High Elves of the West, having been in exile for thousands of years, still honour Varda and the stars above all else. And of course, one star is no star at all but a Silmaril, borne aloft on Eärendil's brow, sailing through the oceans of space on his sky-ship. We know it today as the Evening Star, the Morning Star, Venus.
If you're interested in reading more about the astronomy of Middle-earth, there's a great academic paper by Dr Kristine Larsen of Central Connecticut State University entitled "The Astronomy of Middle-earth," available at theonering.net.