The Houses of Healing
is the thirty-ninth soundtrack of the Complete Recordings of The Lord of the Rings: The Return of the King
It plays in the extended edition of the movie, after the Battle of the Pelennor Fields. Aragorn goes to the Houses of Healing to help Eowyn recover after her fight with the Witch-king of Angmar, healing her injured arm and helping her regain consciousness.
The song is sung by Liv Tyler, giving her character Arwen a bit of connection to the relationship between Aragorn and Eowyn.