Anomaly matching constrains low-energy physics of strongly-coupled field theories. It has been recently extended to the theories with one-form symmetries including SU(N) Yang-Mills theory with theta=pi. In this talk, we show that we develop a systematic procedure for deriving an ’t Hooft anomaly of the circle-compactified theory starting from the anomaly of the original uncompactified theory without one-form symmetries, where the twisted boundary condition for the compactified direction plays a pivotal role. As an application, we consider ZN-twisted CP^N-1 sigma model and massless ZN-QCD, and compute their anomalies explicitly. We also discuss constraints on finite-(T,mu) phase diagram of ZN-QCD based on the anomaly matching.