Actually, Celeborn went to Rivendell to dwell with his grandsons Elladan and Elrohir, after the Ringbearers went West. There's a quote from the Prologue:
Quote:
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It is said that Celeborn went to dwell [in Rivendell] after the departure of Galadriel; but there is no record of the day when at last he sought the Grey Havens, and with him went the last living memory of the Elder Days in Middle-earth.
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So, unless there's information elsewhere, we don't even know if he left Middle-earth.
[ December 28, 2002: Message edited by: Manwe Sulimo ]