The concept of combustion under oxy-fuel conditions has the potential to reduce greenhouse gas emissions. For the design of combustion devices operating under these conditions, a good understanding of fuel oxidation behavior in terms of chemical kinetic mechanisms is useful. For the oxidation of the main component of natural gas and coal devolatilization products, i.e., methane, various chemical mechanisms are available in the literature validated mostly with experiments using air and none of them is developed particularly or has been validated extensively for oxy-methane combustion. An important prerequisite for model assessment is high-quality data typically obtained from resource- and time-consuming measurements. The aim of this study is to identify the best methane mechanism for oxy-fuel combustion from a set of models available in the literature with a minimum number of measurements. Five chemical models, which have been validated for the oxidation of methane/air mixtures, are compared in terms of their performance for extinction strain rates, ignition delay times, and laminar burning velocities of oxy-methane mixtures. A model-based experimental design method, i.e., Akaike weights design criterion, is applied to determine the optimal potential measurements. Ideally, at the conditions of designed experiments, model predictions are nicely separated and, thus, the best model can be identified by comparison to these measurements. It is shown that the employed experimental design strategy identifies informative experiments for model discrimination efficiently. While measurements of extinction strain rates are proposed to be carried out for flames with small methane mass fractions of the fuel stream and oxygen mass fractions of the oxidizer stream, shock tube experiments are evaluated as equally useful for model discrimination over the investigated range of conditions. Measurements of flame speeds are designed at very small and very large equivalence ratios particularly at relatively high pressures.