There still exists a large gap between simulation work and industrial applications in the context of control and optimization of solid-oxide fuel-cell (SOFC) systems. In an effort to bridge this gap, this study describes the experimental implementation of steady-state real-time optimization (RTO) to an SOFC system that consists of both hardware and software components. The proposed adaptive optimization scheme uses an approximate steady-state model of the fuel-cell system and corrects it "appropriately" so that it becomes "excellent" for optimization. This way, the plant can be steered efficiently toward optimality, while meeting the varying electric power demand. In these experiments, the plant efficiency was increased from 55% to 62% through application of RTO. Furthermore, although the SOFC system is characterized by slow thermal dynamics that may take a few hours to settle to steady state, it has been possible to reduce the time necessary to reach the power setpoint from 1 h to about 5 min thanks to the use of transient measurements and a dynamic model. This experimental work has shown that it is possible, not only to control the SOFC system at a desired operating point, but also to operate it near optimality despite changes in power demand.