This book constitutes the proceedings of the 12th International Workshop on Numerical Software Verification, NSV 2019, held in New York City, NY, USA, in July 2019 - colocated with the International Conference on Computer Aided Verification, CAV 2019.The 5 full papers presented together with 2 short papers, 3 abstracts of invited talks, and 2 tutorial papers were carefully reviewed and selected from numerous submissions.The NSV 2017 workshop is dedicated to the development of logical and mathematical techniques for the reasoning about programmability and reliability.