- "At the Grey Havens dwelt Círdan the Shipwright, and some say he dwells there still, until the Last Ship sets sail into the West."
- ― The Lord of the Rings, Appendix A, Eriador, Arnor, and the Heirs of Isildur
Círdan maintained the haven at least into the Fourth Age, but it was recognized that eventually, its purpose would reach an end when no more Elves wished to cross the Sea. At that time, Círdan would abandon the Grey Havens and finally travel the Straight Road himself.
The Last Ship apparently sailed before Fo.A. 120 based on Aragorn's final words to Arwen. Aragorn suggests Arwen might still sail into the West, and one of the reasons she gives that this is impossible is that "There is now no ship that would bear me hence...". This implies that the Last Ship had already sailed by Fo.A. 120, the year in which this conversation took place.
Celeborn eventually sought the Grey Havens, taking with him the last memory of the Elder Days in Middle-earth. Since Círdan and Celeborn are among the only Elves of the Elder Days in Middle-earth, they took the Last Ship together.
 See also