Power overshoot can hinder determination of maximum power densities in microbial fuel cells (MFCs). In this work, a microfluidic approach was used to study overshoot in an MFC containing a pure culture of electroactive biofilms (EAB) containing Geobacter sulfurreducens. After 1-month operation under constant flow of an ideal nutrient medium, the MFC health began to degrade, marked by voltage loss and the appearance of anomalies in the power density curves. One such anomaly was a chronic power overshoot, accompanying a loss of both measured power and current density on the high-current side of the power density curve. The degree of power overshoot was quantified while certain flow-based interventions were applied, notably the shear erosion of the EAB outer layer. Next, two approaches to acclimation were demonstrated to treat the remaining overshoot. The standard approach, which acclimates the MFC to high currents before a standard polarization test, eliminated the remaining overshoot and returned maximum power densities to initial levels, but maximum current density remained lower than the initial level. A microfluidic-assisted “long-hold polarization test” enabled efficient in situ acclimation of each external resistor during the measurement. Despite the health-compromised MFC, this method provided long-term stability during the polarization test, resulting in power and current density measurements that exceeded those made on the healthy MFC using the standard polarization test. We conclude that slower electron transfer kinetics in unhealthy MFCs can provoke overshoot by prolonging the time to reach steady state during the polarization test, but a properly designed measurement overcomes this problem.