This work investigates numerically a catalytic postcombustor for a micro-solid oxide fuel cell (SOFC) system. The postcombustor oxidizes toxic and explosive carbon monoxide (CO) and hydrogen exiting a solid oxide fuel cell to carbon dioxide and water. A single 1 mm diameter monolith reactor channel coated with platinum catalyst is modeled in this work. The inlet stream composition is provided by a semi-analytical 2D model of a detailed SOFC system. The model of the postcombustor includes the 2D axisymmetric Navier–Stokes equations, heat conduction in the channel wall, and a multistep finite-rate mechanism for the surface reactions. It is shown that under the operation conditions considered, the influence of homogeneous (gas phase) reactions can be neglected. The model predicts the expected adiabatic temperatures at the postcombustor outlet correctly and can be used for dimensioning and optimization. Postcombustor performance varies significantly with the choice of the operating parameters of the fuel cell. The most critical molecule at the SOFC outlet is shown to be CO because its depletion is slower than that of for the entire operating range of the SOFC. It can be shown that the postcombustor is able to reduce the level of CO below the toxicity threshold of 25 ppm. Although higher voltages of the fuel cell lead to faster CO conversion in the postcombustor, they also result in a significant increase in wall temperature of the catalyst device. Furthermore, the percentage of SOFC power output used for pump work is lowest for the voltage where the maximum power is reached. For postcombustion the optimal operation point of the SOFC is at the voltage for maximum power of the SOFC system.