Following the disagreement with others in the Tivoli Gardens management, Carstensen travelled to the Danish West Indies and joined the army there. He was married to the daughter of an island planter and assisted in management of the property. He subsequently spent time in New York City where he designed the New York Crystal Palace – an exhibition building constructed for the Exhibition of the Industry of All Nations in 1853 – in collaboration with the German architect Charles Gildemeister.