I will present a new computation of the Wess-Zumino effective action for generic N=1 superconformal field theories in four dimensions using off-shell N=1 conformal supergravity in the components formalism. The result currently includes terms up to second order in the fermions. I will discuss the connection of this result with the superspace expression of Schwimmer and Theisen, and comment on the relation with the supersymmetric Casimir energy and the holomorphicity of the partition function on supersymmetric backgrounds.