Radar altimeters have been measuring ocean significant wave height for more than three decades, with their data used to record the severity of storms, the mixing of surface waters and the potential threats to offshore structures and low-lying land, and to improve operational wave forecasting. Understanding climate change and long-term planning for enhanced storm and flooding hazards are imposing more stringent requirements on the robustness, precision, and accuracy of the estimates than have hitherto been needed. Taking advantage of novel retracking algorithms, particularly developed for the coastal zone, the present work aims at establishing an objective baseline processing chain for wave height retrieval that can be adapted to all satellite missions. In order to determine the best performing retracking algorithm for both Low Resolution Mode and Delay-Doppler altimetry, an objective assessment is conducted in the framework of the European Space Agency Sea State Climate Change Initiative project. All algorithms process the same Level-1 input dataset covering a time-period of up to two years. As a reference for validation, an ERA5-based hindcast wave model as well as an in-situ buoy dataset from the Copernicus Marine Environment Monitoring Service In Situ Thematic Centre database are used. Five different metrics are evaluated: percentage and types of outliers, level of measurement noise, wave spectral variability, comparison against wave models, and comparison against in-situ data. The metrics are evaluated as a function of the distance to the nearest coast and the sea state. The results of the assessment show that all novel retracking algorithms perform better in the majority of the metrics than the baseline algorithms currently used for operational generation of the products. Nevertheless, the performance of the retrackers strongly differ depending on the coastal proximity and the sea state. Some retrackers show high correlations with the wave models and in-situ data but significantly under- or overestimate large-scale spectral variability. We propose a weighting scheme to select the most suitable retrackers for the Sea State Climate Change Initiative programme.