Reliable estimation of the on-site sea state parameters is essential to decision support systems for safe navigation of ships. The wave spectrum can be estimated from procedures based on measured ship responses. The paper deals with two procedures—Bayesian Modelling and Parametric Modelling—which both use complex-valued frequency response functions (FRF) to estimate the wave spectrum. It is therefore interesting to investigate how the filtering aspect, introduced by FRF, affects the final outcome of the estimation procedures. In order to do this, extensive numerical simulations—with known wave parameters—are carried out for a large container vessel. The study shows that filtering has an influence on the estimations, since high-frequency components of the wave excitations are not estimated as accurately as lower frequency components.