Lithium-sulfur (Li-S) batteries are an emerging energy storage technology with higher performance than lithium-ion batteries in terms of specific capacity and energy density. However, several scientific and technological gaps need to be filled before Li-S batteries will penetrate the market at a large scale. One such gap, which is tackled in this paper, is represented by the estimation of state-of-health (SOH). Li-S batteries exhibit a complex behaviour due to their inherent mechanisms, which requires a special tailoring of the already literature-available state-of-charge (SOC) and SOH estimation algorithms. In this work, a model of SOH based on capacity fade and power fade has been proposed and incorporated in a state estimator using dual extended Kalman filters has been used to simultaneously estimate Li-S SOC and SOH. The dual extended Kalman filter’s internal estimates of equivalent circuit network parameters have also been used to the estimate maximum available power of the battery at any specified instant. The proposed estimators have been successfully applied to both fresh and aged Li-S pouch cells, showing that they can accurately track accurately the battery SOC, SOH, and power, providing that initial conditions are suitable. However, the estimation of the Li-S battery cells’ capacity fade is shown to be more complex, because the practical available capacity varies highly with the applied current rates and the dynamics of the mission profile.