Efficiency, reliability and lifetime of polymer electrolyte membrane fuel cells (PEMFCs) are significantly limited by inadequate water management. High-performance water active control algorithms cannot be implemented due to the absence of adequate online sensors that can measure the internal liquid water saturation. A promising technique that can be applied in this context is the state observer. However, fuel cell models present strong nonlinearities, model uncertainty, unmatched unknown parameters and sensor noise, which are major difficulties in observer design. The algorithm proposed in this work is based on a time-varying adaptive observer, that offers an estimation of the liquid water state and behaviour in the cathode catalyst layer of a PEMFC, coupled with a low-power peaking-free observer with dynamic dead-zone filtering that is used as a high-performance soft sensor. The algorithm is shown to provide an accurate estimation of the liquid water saturation and the liquid water transport parameters even in the presence of sensor noise and model inaccuracies. The results are validated through numerical simulations and in a real experimental prototype. This work has been partially funded by the Spanish State Research Agency through the María de Maeztu Seal of Excellence to IRI (MDM-2016-0656) and by the project DOVELAR (ref. RTI2018-096001-B-C32).