I realize this is stretching the lore just a tad, since Aragorn has the sword in TA 2965, but let's say, for the sake of making a fun adventure, the remaining shards themselves are still being held in Rivendell.
My players have just finished the Star of the Mist, and after a council with Sabian, have agreed to take him and a handful of his men to Rivendell, not realizing that he is one of the Black Númenóreans from Ruins of the Lost Realm. The players are in the midst of their first Fellowship Phase in Bree, and Sabian and his men are staying in the Chetwood to avoid too many prying eyes and questions from Bree-landers.
My thought is, if they take these men to Rivendell without issue and stay more than a day or so, Sabian may try to sneak away with the remaining shards of Narsil in an attempt to ensure the blade that cut the One Ring off the hand of Sauron could never be reforged (as a bonus to finding the valley of Imladris itself).
Where I need a little help is, how would you all play this scenario from there? Would you boil it down to a simple Hunting roll or skill endeavor to try to find Sabian? It seems anti-climactic, but I'm having trouble figuring out how else I might make this engaging for my players beyond this.