In this article, a process for sorption-enhanced steam methane reforming in an adiabatic fixed-bed reactor coupled with a solid oxide fuel cell (SOFC) is evaluated using a 1D numerical reactor model combined with a simplified fuel cell simulation. A novel material comprising CaO/CuO/Al2O3(NiO) pellets is considered. Three operating stages are considered in the proposed system, namely (i) CaO carbonation/reforming, (ii) Cu and Ni oxidation, and (iii) CaCO3 calcination/CuO and NiO reduction. The operating conditions that enable cyclic operation of these stages and the strategy needed to switch between each stage are evaluated. Under the adopted control strategy, methane conversion was about 95%, whilst H2 yield and purity were around 3.2 molH2 molCH4−1 and 90%, respectively. Moreover, a concentrated CO2 stream ready for storage was obtained. By using a portion of the produced H2 to make the process self-sufficient from an energy standpoint, an equivalent H2 yield and a reforming efficiency of about 2.8 molH2 molCH4−1 and 84% were achieved, respectively. With respect to SOFC integration, net power and thermal energy generation of around 11 kW and 6 kW, respectively, can be achieved. With respect to the chemical energy of the inlet methane, the net electrical and thermal efficiencies of the considered process are 56% and 30%, respectively, i.e., the overall efficiency of the entire system is 86%. The proposed cogeneration system showed better thermodynamic, environmental and economic performances than those of conventional systems, with an investment pay-back period of 2.2 years in the worst-case scenario. The levelised cost of electricity, of heat and total power were about 0.096 € kW h−1, 0.19 € kW h−1, and 0.065 € kW h−1, respectively, while the CO2 emissions were avoided at no cost.