This book constitutes the refereed proceedings of the 12th International Conference on Verified Software, VSTTE 2020, and the 13 International Workshop on Numerical Software Verification, NSV 2020, held in Los Angeles, CA, USA, in July 2020. Due to COVID-19 pandemic the conference was held virtually. The 13 papers presented in this volume were carefully reviewed and selected from 21 submissions. The papers describe large-scale verification efforts that involve collaboration, theory unification, tool integration, and formalized domain knowledge as well as novel experiments and case studies evaluating verification techniques and technologies. The conference was co-located with the 32nd International Conference on Computer-Aided Verification (CAV 2020).