Innovative structured catalyst supports, like solid foams, wire gauzes, and short-channel structures, are considered in methane catalytic combustion. For comparison, classical supports such as packed beds and monoliths are also taken into account. Moreover, two catalysts, displaying "fast" and "slow" kinetics, are examined. The performance efficiency criterion is applied to account for a balance between the process conversion, mass transfer, and flow resistance. Another "technological" approach compares reactor length and the corresponding pressure drop required to reach the desired conversion rate. Results indicate that wire gauze, solid foam, and short-channel structure are highly promising catalyst supports due to their intense heat/mass transfer and moderate flow resistance, particularly for fast catalytic reactions. For slow reactions, monoliths seem to be the best as they exhibit the lowest flow resistance.