In the field of multicriteria decision aid, the Simos method is considered as an effective tool to assess the criteria importance weights. Nevertheless, the method's input data do not lead to a single weighting vector, but infinite ones, which often exhibit great diversification and threaten the stability and acceptability of the results. This paper proves that the feasible weighting solutions, of both the original and the revised Simos procedures, are vectors of a non-empty convex polyhedral set, hence the reason it proposes a set of complementary robustness analysis rules and measures, integrated in a Robust Simos Method. This framework supports analysts and decision makers in gaining insight into the degree of variation of the multiple acceptable sets of weights, and their impact on the stability of the final results. In addition, the proposed measures determine if, and what actions should be implemented, prior to reaching an acceptable set of criteria weights and forming a final decision. Two numerical examples are provided, to illustrate the paper's evidence, and demonstrate the significance of consistently analyzing the robustness of the Simos method results, in both the original and the revised method's versions.