Why didnt Celeborn go with......

[zifnab]

Why didn't Celeborn go with Bilbo, Frodo, Gandalf, Elrond and Galadriel to the Grey Havens, and pass over the sea? I know the above were ring-bearers(and Celeborn was not), and that is why they went but it also says:

Then Elrond and Galadriel rode on; for the Third Age was over, and the Days of the Rings were passed, and an end was come of the story and song of those times. With them went many Elves of the High Kindred who would no longer stay in Middle-Earth;and among them, filled with a sadness that was yet blessed and without bitterness, rode Sam, and Frodo, and Bilbo, and the Elves delighted to honour them.

I believe that Celeborn was a kinsman of Thingol. Was he not of a high enough kindred to go with them, or did he stay behind for other reasons?