The BioModels Repository contains over 1000 manually curated mechanistic models drawn from published literature, most of which are encoded in the Systems Biology Markup Language (SBML). This community-based standard formally specifies each model, but does not describe the computational experimental conditions to run a simulation. Therefore, it can be challenging to reproduce any given figure or result from a publication with an SBML model alone. The Simulation Experiment Description Markup Language (SED-ML) provides a solution: a standard way to specify exactly how to run a specific experiment that corresponds to a specific figure or result. BioModels was established years before SED-ML, and both systems evolved over time, both in content and acceptance. Hence, only about half of the entries in BioModels contained SED-ML files, and these files reflected the version of SED-ML that was available at the time. Additionally, almost all of these SED-ML files had at least one minor mistake that made them invalid. To make these models and their results more reproducible, we report here on our work updating, correcting and providing new SED-ML files for 1055 curated mechanistic models in BioModels. In addition, because SED-ML is implementation-independent, it can be used for verification, demonstrating that results hold across multiple simulation engines. Here, we use a wrapper architecture for interpreting SED-ML, and report verification results across five different ODE-based biosimulation engines. Our work with SED-ML and the BioModels collection aims to improve the utility of these models by making them more reproducible and credible.