This book constitutes the refereed proceedings of the 13th International Conference on Verified Software, VSTTE 2021, and the 14th International Workshop on Numerical Software Verification, NSV 2021, held online, in July/ October 2021. Due to COVID-19 pandemic the conference was held virtually. There were 10 papers presented in this volume were carefully reviewed and selected from 20 submissions. The papers focuses on challenges of the verification of cyber-physical systems with machine learning components and making large-scale verified software a practical reality and much more.