There are only 38 paintings and costume made pieces of Baur known, of which 28 have the sea and the water as a subject. In 1807, Louis Napoleon the King of Holland at that time bought two paintings by this master Harlingen for his private collection.

National fame, however, came a year later in 1808 when Baur won f 3000 for a sea piece submitted by him on the ”Exhibition of living masters ” organized in the Royal Palace.  In later years, the Rijksmuseum in Amsterdam also bought work from the artist. In 1827 they purchased four paintings with scenes from the bombing of the North African city of Algiers for the sum of f 2000.

Baur also regularly took part in exhibitions organized by the Koninklijk Instituut in Amsterdam and following this was written in 1816 the subsequent critical praise: ”Als zeeschilder, echter, is hij de eerste van zijn vak. Zijn water is dun, en fraai van toon en golving; zijnen schepen zijn juist, en zijne luchten zeer goed… Bauer is een groot man.”