Neilson was a benefactor of the Metropolitan Museum of Art, to which he donated several paintings, including "A Winter Carnival in a Small Flemish Town", "Portrait of a Man, Possibly George Frederick Handel", and "The Pelkus Gate near Utrecht". Neilson's late wife, Helen Swift Neilson, had bequeathed "Portrait of a Young Woman with a Fan", by Rembrandt, for which she had paid $250,000 in 1930; "Rembrandt Harmensz" (Dutch, 1606–1669); the "Portrait of Mrs. Thomas Pechell", and "1799". The Boston Museum of Fine Arts was given John Singer Sargent's painting "A Capriote". The Liverpool Cathedral also received support from Neilson in the form of a collection of Organ and Choral Works which he sponsored; the organ at the Cathedral also bears his name.