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.