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The answer appears in Tolkien's The Road Goes Ever On

"The question Sí man i yulma nin enquantuva? and the question at the end of her song (Vol. I, p. 389), What ship would bear me ever back across so wide a Sea?, refer to the special position of Galadriel.
She was the last survivor of the princes and queens who had led the revolting Noldor to exile in Middle-earth. After the overthrow of Morgoth at the end of the First Age a ban was set upon her return, and she had replied proudly that she had no wish to do so. She passed over the Mountains of Ered Luin with her husband Celeborn (one of the Sindar) and went to Eregion.
But it was impossible for one of the High-Elves to overcome the yearning for the Sea, and the longing to pass over it again to the land of their former bliss. She was now burdened with this desire.
In the event, after the fall of Sauron, in reward for all that she had done to oppose him, but above all for her rejection of the Ring when it came within her power, the ban was lifted, and she returned over the Sea, as is told at the end of The Lord of the Rings."

_{JRRT, The Road Goes Ever On, 1967}

So while a lot of posthumously published material exists about Galadriel, this is the explanation that Tolkien himself chose to reveal to readers, published in 1967.

The answer appears in Tolkien's The Road Goes Ever On

"The question Sí man i yulma nin enquantuva? and the question at the end of her song (Vol. I, p. 389), What ship would bear me ever back across so wide a Sea?, refer to the special position of Galadriel.

She was the last survivor of the princes and queens who had led the revolting Noldor to exile in Middle-earth. After the overthrow of Morgoth at the end of the First Age a ban was set upon her return, and she had replied proudly that she had no wish to do so. She passed over the Mountains of Ered Luin with her husband Celeborn (one of the Sindar) and went to Eregion.

But it was impossible for one of the High-Elves to overcome the yearning for the Sea, and the longing to pass over it again to the land of their former bliss. She was now burdened with this desire.

In the event, after the fall of Sauron, in reward for all that she had done to oppose him, but above all for her rejection of the Ring when it came within her power, the ban was lifted, and she returned over the Sea, as is told at the end of The Lord of the Rings."

_{JRRT, The Road Goes Ever On, 1967}

So while a lot of posthumously published material exists about Galadriel, this is the explanation that Tolkien himself chose to reveal to readers, published in 1967.

The answer appears in Tolkien's The Road Goes Ever On

"The question Sí man i yulma nin enquantuva? and the question at the end of her song (Vol. I, p. 389), What ship would bear me ever back across so wide a Sea?, refer to the special position of Galadriel. She was the last survivor of the princes and queens who had led the revolting Noldor to exile in Middle-earth. After the overthrow of Morgoth at the end of the First Age a ban was set upon her return, and she had replied proudly that she had no wish to do so. She passed over the Mountains of Eredluin with her husband Celeborn (one of the Sindar) and went to Eregion. But it was impossible for one of the High-Elves to overcome the yearning for the Sea, and the longing to pass over it again to the land of their former bliss. She was now burdened with this desire. In the event, after the fall of Sauron, in reward for all that she had done to oppose him, but above all for her rejection of the Ring when it came within her power, the ban was lifted, and she returned over the Sea, as is told at the end of The Lord of the Rings."

JRRT, The Road Goes Ever On, 1967

So while a lot of posthumously published material exists about Galadriel, this is the explanation that Tolkien himself chose to reveal to readers, published in 1967.

The answer appears in Tolkien's The Road Goes Ever On

"The question Sí man i yulma nin enquantuva? and the question at the end of her song (Vol. I, p. 389), What ship would bear me ever back across so wide a Sea?, refer to the special position of Galadriel. 
She was the last survivor of the princes and queens who had led the revolting Noldor to exile in Middle-earth. After the overthrow of Morgoth at the end of the First Age a ban was set upon her return, and she had replied proudly that she had no wish to do so. She passed over the Mountains of Ered Luin with her husband Celeborn (one of the Sindar) and went to Eregion.
But it was impossible for one of the High-Elves to overcome the yearning for the Sea, and the longing to pass over it again to the land of their former bliss. She was now burdened with this desire.
In the event, after the fall of Sauron, in reward for all that she had done to oppose him, but above all for her rejection of the Ring when it came within her power, the ban was lifted, and she returned over the Sea, as is told at the end of The Lord of the Rings."

_{JRRT, The Road Goes Ever On, 1967}

So while a lot of posthumously published material exists about Galadriel, this is the explanation that Tolkien himself chose to reveal to readers, published in 1967.

The answer was published by Tolkien in The Road Goes Ever On, in 1967:

"The question Sí man i yulma nin enquantuva? and the question at the end of her song (Vol. I, p. 389), What ship would bear me ever back across so wide a Sea?, refer to the special position of Galadriel. She was the last survivor of the princes and queens who had led the revolting Noldor to exile in Middle-earth. After the overthrow of Morgoth at the end of the First Age a ban was set upon her return, and she had replied proudly that she had no wish to do so. She passed over the Mountains of Eredluin with her husband Celeborn (one of the Sindar) and went to Eregion. But it was impossible for one of the High-Elves to overcome the yearning for the Sea, and the longing to pass over it again to the land of their former bliss. She was now burdened with this desire. In the event, after the fall of Sauron, in reward for all that she had done to oppose him, but above all for her rejection of the Ring when it came within her power, the ban was lifted, and she returned over the Sea, as is told at the end of The Lord of the Rings."

JRRT, The Road Goes Ever On, 1967

So while there is plenty of confusing material in posthumously published material (texts or notes Tolkien himself never published), or in this letter or that letter, this is the explanation that the author himself chose to reveal to his readers.

Not surprisingly, a letter also dated 1967 appears to agree, in which JRRT wrote: "The Exiles were allowed to return - save for a few chief actors in the rebellion of whom at the time of L.R. only Galadriel remained."

But in any case it's the explanation in The Road Goes Ever On which was authorized by JRR Tolkien himself for publication.

The answer appears in Tolkien's The Road Goes Ever On

"The question Sí man i yulma nin enquantuva? and the question at the end of her song (Vol. I, p. 389), What ship would bear me ever back across so wide a Sea?, refer to the special position of Galadriel. She was the last survivor of the princes and queens who had led the revolting Noldor to exile in Middle-earth. After the overthrow of Morgoth at the end of the First Age a ban was set upon her return, and she had replied proudly that she had no wish to do so. She passed over the Mountains of Eredluin with her husband Celeborn (one of the Sindar) and went to Eregion. But it was impossible for one of the High-Elves to overcome the yearning for the Sea, and the longing to pass over it again to the land of their former bliss. She was now burdened with this desire. In the event, after the fall of Sauron, in reward for all that she had done to oppose him, but above all for her rejection of the Ring when it came within her power, the ban was lifted, and she returned over the Sea, as is told at the end of The Lord of the Rings."

JRRT, The Road Goes Ever On, 1967

So while a lot of posthumously published material exists about Galadriel, this is the explanation that Tolkien himself chose to reveal to readers, published in 1967.