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We investigated several viable options for combining a gas turbine and a solid oxide fuel cell to achieve very high power generation efficiency. The backbone of the combination is the solid oxide fuel cell/gas turbine dual combined cycle and the solid oxide fuel cell/gas and steam turbine triple combined cycle. The object of analysis is central power plants on the order of hundreds of MW. The gas turbine parameters were taken from an F-class commercial engine, and state-of-the-art parameters of the SOFC were used. In each of the two cycles, the use of a recuperative heat exchanger was considered as a design option. The performance of the combined cycles using the commercial gas turbine was estimated in the first part of the study, and optimal design performance was predicted in the second part assuming a completely revised gas turbine design. Overall, the triple combined cycle was expected to provide better efficiency than the dual combined cycle. Its optimal efficiency was predicted to be over 75%, which is about three percentage points higher than that of the dual combined cycle. The optimal efficiencies of the recuperated and non-recuperated systems were almost the same, which provides flexibility in selecting a system configuration.