The experimental validation of a real-time optimization (RTO) strategy for the optimal operation of a solid oxide fuel cell (SOFC) stack is reported in this paper. Unlike many existing studies, the RTO approach presented here utilizes the constraint-adaptation methodology, which assumes that the optimal operating point lies on a set of constraints and then seeks to satisfy those constraints in practice via bias update terms. These biases correspond to the difference between predicted and measured outputs and are updated at each steady-state iteration, allowing the RTO to successfully meet the optimal operating conditions of a 6-cell SOFC stack, despite significant plant-model mismatch. The effects of the bias update filter values and of the RTO frequency on the power tracking and constraint handling are also investigated.