© 2016 Elsevier Ltd. Variance-based global sensitivity analysis (e.g., the Sobol' sensitivity index) can be used to identify the important parameters over the entire parameter space. However, one often cannot afford the computational costs of sampling-based approaches in combination with expensive high-fidelity forward models. Reduced-order models (ROM) can substantially accelerate calculation of these sensitivities. However, it is usually difficult to determine what type of ROM should be used and how accurately the ROM represents the high-fidelity model (HFM) results. In this paper, we propose to concurrently use multiple ROMs as a way to assess the robustness of the model-reduction method. Two sets of HFM simulations are needed, one set for building ROMs and the other for validating ROMs. Our goal is to keep the total number of HFM simulations to a minimum. Ideally some of the HFM simulations in the first set can be shared by different ROMs. Based on validation results, the ROMs can be combined with different schemes. We demonstrate that we can achieve the goal by using four different ROMs and still considerably save computational time compared to using traditional HFM simulation for calculating sensitivity indices. We apply the approach to an example problem of a large-scale geological carbon dioxide storage system, in which the objective is to calculate a sensitivity index to identify important parameters. For this problem, the locally best ROM provides better estimates than the weighted average from all ROMs.