An activated-carbon electric-double-layer capacitor is characterized and an adaptive algorithm is derived and implemented that is commensurate with potential traction applications of these energy storage devices. The electrochemical characterization relies on a simplified equivalent circuit interpretation extracted from a more-complete mathematical representation of the capacitor system. In addition to the high power capability and potentially low costs of this class of capacitors, we clarify the substantial invariance of the device performance with respect to temperature, a distinct advantage over battery systems. The robustness of the equivalent circuit in terms of capturing the salient features of the experimental data over the temperature and voltage range of interest enables the formulation of a model-reference adaptive algorithm. The algorithm developed and implemented in this work is fully recursive in that the only variables required for on-line regression are those of the previous time step and the current time step. Successful comparisons of the algorithm's adapted state of charge and power predictions provide an initial validation of the algorithm.