We know what happened to the Silmaril reclaimed by Beren and Luthien: all of Middle-earth can see it when they look up at dawn or dusk. And we know what happened to the other two after Morgoth was overthrown, because... uh... why, again? I mean, there were only two witnesses to Maedhros throwing one into the fires (and one was Maedhros himself, who's dead). And there was only one witness fo Maglor throwing the second into the sea. So what if Maglor lied? How does the story we know change?
First up: what happened to Maedhros? It could be they went their separate ways, with Maglor's story just a way to stop people looking for his brother, but I think it more likely the two fought, and Maedhros was killed - the last in a long line of kinslayings. Then Maglor has two Silmarilli, but they burn him; moreover, he's just killed his last brother over the things. He doesn't want them any more. But what can he do with them, without breaking his oath and drawing down the judgement of Iluvatar?
The very Tolkien answer is, he has to keep them in the family. But his brothers are dead, and his only nephew, Celebrimbor, a) doesn't want anything to do with him, b) is kind of disowned, and c) is way too much like Feanor to be trusted with the Jewels. But... but Maglor has two children of his own. Adopted children.
So he passes the Silmarilli to Elrond and Elros, trusting them to keep them secret and safe. It's almost as good an ending to their tale as Tolkien's: a final Kinslaying, a repentance, and finally all three Jewels are in the hands of the house of Eärendil. One travels to Númenor with Elros, while the other goes with Elrond to Lindon, in the Blue Mountains. Water, earth, and sky, just like Tolkien said.
But Middle-earth doesn't end with the First Age.
The Land of Gift
In Númenor, the Silmaril is one of the many treasures of the royal house, kept hidden. As the nation declines, the kings begin to look at it with desire rather than reverence - but they know they can't touch it, lest it burn them.
Then comes Ar-Pharazôn the Usurper. He travels to Middle-earth, warring against Sauron - and takes the Dark Lord prisoner. The servant of Morgoth is brought back to Númenor... and he senses the Light hidden there.
There's no question that Sauron would want the Silmaril, but he's a prisoner. It takes him a very long time to seduce Ar-Pharazon into burning the White Tree, the other symbol of the Light; it would take longer to persuade him to surrender a treasure. Simpler by far to wait until the king's attack on Aman has failed, and simply take what he wants.
But there is another player at work. Amandil, Lord of Andúnië, has already persuaded his grandson Isildur to sneak into the palace and steal a cutting of the White Tree. Now he has his own plans to be a second Eärendil - to sail West and seek the aid of the Valar. And how did Eärendil safely reach Aman? By carrying his wife's Silmaril.
Amandil, or one of his relatives, steals the Silmaril. Amandil boards his ship with his three servants, and sails into the West. And there his story, and the story of the second Silmaril, finds its unknown end. Was he turned back, to flounder in the Great Sea? Or did he attain his goal, returning the Jewel to the Blessed Realm? We simply don't know.
Numenor falls. Sauron flees, disincarnate, back to Middle-earth. But now he knows that the Silmarils are not as lost as everyone thought - and he has a decent guess at where the last of them is held.
The Last of Beleriand
Elrond, we know, followed Gil-Galad after the War of Wrath, setting up the kingdom of Lindon in the last scraps of Beleriand west of the Blue Mountains. He became the High King's herald and second-in-command, rendering to him all fealty... and it seems likely that he would also have yielded up the Silmaril to his liege, Gil-Galad, 'the Star of Radiance'.
The countless stars of heaven's field
Were mirrored in his silver shield.
All through the Second Age, Gil-Galad held the Silmaril in trust. His closest ally was Celebrimbor in Eregion, but he absolutely could not tell the grandson of Feanor what he had - the shadow of the Kinslayings still lay over their relationship. He barred the gates of Lindon before 'Annatar', unsure of the Maia's alliegence, and unwilling to let any of that people into range of the Jewel. When he gifted his two Rings of Power to Cirdan and Elrond, he kept the Jewel for himself.
And Lindon flourished, as southern Ossiriand had when Beren and Luthien stayed there. But the Second Age drew on, and war with Sauron loomed: the last war, a Last Alliance in the face of his darkness.
Did Gil-Galad set the Silmaril in his shield? Did he mount it in the head of his great spear Aeglos, the Snow-Point? Or did he set it on his brow, a beacon of ancient light as he marched to war?
In the end, it doesn't matter which he chose:
For into darkness fell his star
In Mordor, where the shadows are.
For one brief moment, Sauron claimed the Silmaril of Gil-Galad, on the slopes of Orodruin itself. But it burned him, and perhaps contributed to his defeat and destruction at Isildur's hands. For the second time in his life, Isildur took possession of a Jewel of Feanor.
The Third Age
Did he hide it from Elrond and Cirdan, even as they begged him to destroy the Ring? Or did they know he had it? One thing is sure: he would never give it up. Perhaps he offered to bear it back to Lindon for them, never intending to keep his promise. The Silmaril was his now, as the other two had been his ancestors'.
So Isildur rode north, and in the Gladden Fields he was ambushed. The Silmaril, carried secretly in a pocket, fell into Anduin with his body. Smeagol never found it (and a good thing, too; he would have been destroyed for sure). For thousands of years, it stayed with the king's body.
But that body was eventually found. Saruman dredged it from the river, taking the treasures of Isildur for himself. He claimed the Elendilmir, the white gem set in mithril which marked the High King of the Dunedain; he claimed also the glowing Silmaril. All through the War of the Ring, he carried it with him, while Saruman's robes shimmered with shifting light.
Then Saruman was driven out. The Silmaril was his most precious treasure - he would have taken it with him as he left, perhaps hoping in some secret part of his mind that he could use it to buy his way back into Aman. But if so, he was disappointed: the rogue Maia was killed by his servant, his body vanishing with the wind.
So the last Silmaril ended up in the very place the first printed tale of Middle-earth began: the garden of Bag End Under-Hill. Did Frodo deduce its true nature when he found it, or did he think it another jewel like the famous Arkenstone? Either way, he would have been wary of it, and unwilling to take it for himself: he had had quite enough of magic jewellery by that time. No, the Silmaril would be lifted up, glowing gently, by the rough hands of the humblest of Tolkien's heroes: Samwise Gamgee.
And he wouldn't have kept it. This is Sam we're talking about! He would have sought for some suitable place to lay the 'elven-gem' to rest - and what could be more suitable than to pair it with the Lady Galadriel's gift, burying it in the soft earth beside the silver nut he planted to replace the Party Tree.
At long last, the Light of the Two Trees found its true expression again: gleaming in the golden leaves of the only mallorn west of the Mountains and east of the Sea.