This book constitutes the refereed proceedings of the 13th International Conference on Tests and Proofs, TAP 2019, held as part of the Third World Congress on Formal Methods 2019, Porto, Portugal, in October 2019. The 10 regular papers and 2 invited paper presented in this volume were carefully reviewed and selected from 19 submissions. The TAP conference promotes research in verification and formal methods that targets the interplay of proofs and testing: the advancement of techniques of each kind and their combination, with the ultimate goal of improving software and system dependability.