I agree with Veronwe that it would seem most likely that as the last/next highest-ranked member of the Sindar that Celeborn departed with Cirdan's last ship, but who knows.
Even if he lingered in Imladris or elsewhere even after the passing of Arwen (long before which time her brothers would themselves most certainly have departed or become mortal like her), Celeborn ultimate had to go into the West.
Some Silvan elves (those most akin to Avari rather than Nandorin) may have stayed, but as a true Eldar, Celeborn was destined to depart, along with all the rest via the Grey Havens, such as Thranduil, Galdor and all of the Grey/Green-Elves.
Some Silvan or partially Silvan Elves like Legolas (I'm presuming that Thranduil's wife might have been Nandorin) may have still sailed down Andiun or left from Dol Amroth for some while after Cirdan's last Grey Haven's ship. Unlike his earlier ritings, Tolkien I think dropped the idea that Elves continued to sail over until the present time, but rather that some Silvan and especially the true East-Elves merely stayed and faded into the background, not unlike Hobbits and Dwarves.
As for what Celeborn says to Aragorn, I think he is merely supporting Aragorn's desire to marry his granddaughter, and (perhaps unwittingly) foreshadowing that he and Galadriel will be separated for awhile ere his end in Middle-Earth. Or possibly, he is referring to Elrond and Celebrian.
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The hoes unrecked in the fields were flung, __ and fallen ladders in the long grass lay __ of the lush orchards; every tree there turned __ its tangled head and eyed them secretly, __ and the ears listened of the nodding grasses; __ though noontide glowed on land and leaf, __ their limbs were chilled.
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