Greenhouse gases are released during various industrial processes. Use of CO and CO2 in methanation processes reduces the negative impact of greenhouse gases on the environment and promotes conversion of COx into added value products (such as methane). Performance of methanation processes largely depends on specific inlet gas parameters, operational process parameters and reactor parameters. Besides, selection of a catalyst is of special importance since the performance of various catalysts at constant process parameters differs. Process temperature, H2/COx ratio and catalyst stability have the largest influence on catalyst efficiency in enhancing the COx conversion and CH4 selectivity. The paper demonstrates application of technique for order preference by similarity to ideal solution (TOPSIS) in selection of preferred catalyst with respect to CH4 selectivity. Technical and economic performance is evaluated. The results show that Ru-based catalysts are the preferred alternative for methanation processes, as they show the highest technical and economic performance. In addition, it is demonstrated that multi-criteria analysis can be used as a convenient approach for selecting the preferred catalyst, especially in cases when the research aim is to study the COx reduction via methanation processes and when the availability of resources for experiments is limited.