In this talk, I provide an overview of my research in surrogate model error estimation and code verification for examples in computational mechanics. For the first part of this talk, I present an approach to engineer features that, with machine-learning regression, can accurately predict the error incurred by reduced-order models and other approximations to parameterized systems of nonlinear equations. In the second part of this talk, I discuss our approaches to code verification for hypersonic flow in thermochemical nonequilibrium.