Zwiep became a pastor in Enschede in 1929 and was a well-known figure in the town. On Sunday 19 April 1942, he spoke out in a sermon against National Socialism and the persecution of the Jews. The following day he was arrested by the Germans and after five months of interrogation in prison in Arnhem and Amersfoort he was transported to Dachau. On 24 November 1942, two months after his arrival at the camp, he died of exhaustion and malnutrition.
The biggest Scout group in Enschede is named in Zwiep's memory.
A street in Oostzaan, North Holland, a town where Zwiep worked as pastor from 1924–1927, bears his name - the "Dominee Nanne Zwiepsingel". On 4 May 1978, Oostzaan erected a monument dedicated to the reverend, consisting of a bronze statue of a chair with a chained bird.