<p>This book constitutes the refereed proceedings of the 12th International Conference on Verified Software, VSTTE 2020, and the 13^th 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.<br> 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.<br> The conference was co-located with the 32nd International Conference on Computer-Aided Verification (CAV 2020).</p>