Reduced chemical kinetic models are often used in place of a detailed mechanism because of the computational expense of solving the complete set of equations describing the reacting system. Mathematical methods for model reduction are usually associated with a nominal set of reaction conditions for which the model is reduced. The important effects of variability in these nominal conditions are often ignored because there is no convenient way to deal with them. In this work, we introduce a method to identify rigorous valid ranges for reduced models; i.e., the reduced models are guaranteed to replicate the full model to within an error tolerance under all conditions in the identified valid range. Previous methods have estimated valid ranges using a limited set of variables (usually temperature and a few species compositions) and cannot guarantee that the reduced model is accurate at all points in the estimated range. The new method is demonstrated by identifying valid ranges for models reduced from the GRI-Mech 3.0 mechanism with 53 species and 325 reactions, and a truncated propane mechanism with 94 species and 505 reactions based on the comprehensive mechanism of Marinov et al. A library of reduced models is also generated for several prespecified ranges composing a desired state space. The use of these reduced models with error control in reacting flow simulations is demonstrated through an Adaptive Chemistry example. By using the reduced models in the simulation only when they are valid the Adaptive Chemistry solution matches the solution obtained using the detailed mechanism.