This book constitutes the thoroughly refereed post-conference proceedings of the 13th International Workshop on Coalgebraic Methods in Computer Science, CMCS 2016, colocated with ETAPS 2016, held in Eindhoven, The Netherlands, in April 2016. The 10 revised full papers were carefully reviewed and selected from 13 submissions. Also included are an invited paper and two keynote talks. The papers cover a wide range of topics in the theory, logics and applications of coalgebras.