The Evenstar Necklace
If you've read the books, then you know that "love" isn't really a word that appeared all that much, and that "a love story" is probably one of the last ways you'd describe Tolkien's masterpiece… unless you called The Lord of the Rings "a love story between an Oxford scholar, mythology, and imagined languages."
Nonetheless, Aragorn and Arwen's relationship is a real part of the original story (though it's relegated to the appendices), and is certainly an important feature of the films—everyone loves a Hollywood romance between an ethereal immortal elf woman and her hunky semi-godlike king man. And while Arwen is mostly absent from The Two Towers (aside from some dreamy flashbacks and her talk with her father), we're reminded of her by the gift she gave to Aragorn, the Evenstar necklace.
As far as we know, this necklace has no special, magical elven properties. But, while it doesn't contain immortality, it does represent the eternal promise of love that Arwen has made to Aragorn. Even when Aragorn tries to give it back, saying "this belongs to you," she insists that "it was a gift. Keep it."
A promise of eternal love is a pretty big deal in human time—we're talking fifty-plus years of listening to the same person chuckle over Key and Peele sketches. And in Dúnedain years eternal love might be two or three times as long… and in elven years it's infinity. We think that's pretty special.
Erwin also knows the necklace (and the promise it represents) is pretty special, and it makes her sad because she maybe sort of has a thing for Aragorn. The Evenstar necklace shows that he belongs to someone else—someone important enough to him that he wears a girly piece of jewelry, even though he's a rough and tough fighting man. Maybe Arwen can't be with Aragorn in person, but she's with him in spirit and in often-replicated necklace form.