I had this situation in my game as well, when we were playing through Tales from Wilderland. One of my players, Jamie, made a female Elf of Mirkwood character, a Scholar named Míriel who had gotten herself exiled from the Elven Realm by teaching herself Quenya and then teaching it to others, against the edict of Thranduil. Another player, John, created a Woodman character, also a Scholar, Grundwald, who was basically an autistic savant: incredibly skilled at Lore and Healing (and with his long bow) but almost zero social skills. Jamie decided to leave the game after the adventure with Lady Irimë, to focus on her writing. Grundwald, who was at the time only 16, confessed his adoration of Míriel just as she left with Irimë for Rivendell. 18 months later, after the first adventure of Ruins of the North, which ends in Rivendell, they met again.
I knew John had decided Grundwald’s story-arc was almost over, and he wanted to make a Ranger character for Ruins. I invited Jamie back for a wrap-up session, and she agreed. She and John clearly wanted their characters to end up together. I decided Míriel had been living in Rivendell all that time, and had sent Grundwald a manuscript of the Lay of Leithian indicating her mutual interest in him. There were plenty of Eldar in Rivendell, not least of them Elrond himself, who perceived her thoughts well enough to warn her against a romance with a mortal. It was pointless, they told her, for an Elf to become attached to any particular mortal, as pointless as becoming attached to a butterfly. Worse than pointless, they assured her; it would only mean more suffering for both herself and for the mortal, once the mortal’s brief life-span came to an end. (I decided that there was no reason why ordinary Elves should be offered the choice of becoming mortal themselves.)
Additionally, I told Jamie that Elrond, though as gracious and generous a host as could be imagined, had made it clear that there was no room in Rivendell for an Elf-Mortal romance. Similarly, I told John that his Patron, Radagast, would never allow him back to Rhosgobel with an Elven wife. So when Grundwald arrived in Rivendell, they made their choice. After he scribed a document containing everything he knew about Healing (John had put almost all his Advancement points into that and Lore), he and Míriel chose exile and left together. I was pretty happy with how that wrapped up.