Stochastic programming (SP) is a well-studied framework for modeling optimization problems under uncertainty. However, despite the significant advancements in solving large SP models, they are not widely used in industrial practice, often because SP solutions are difficult to understand and hence not trusted by the user. Unlike deterministic optimization models, SP models generally involve recourse variables that can take different values for different scenarios (i.e. uncertainty realizations), which makes interpreting their solutions a challenge when large numbers of scenarios and recourse variables are considered. In this work, we propose scenario and recourse reduction methods that can help enhance the explainability of SP solutions. Focusing on two-stage linear SP, the goal is to build reduced models, with much smaller sets of scenarios and recourse variables, that are easier to analyze yet still capture the key features of the original problems. Specifically, we explicitly search for reduced models that generate the same or close to the same first-stage decisions as the original SP models. The efficacy of the proposed methods is demonstrated in computational case studies involving problems of industrial relevance and size.