The paper presents a study of the extreme value statistics related to airgap measurements on a scale model of a semisubmersible platform subjected to random waves in a wave basin. Relative wave elevation records corresponding to totally 24 h storm duration are considered, made up by realizations. The focus is on a comparison of two alternative methods for the prediction of extreme values from finite recordings at two different locations at the platform. One is a standard method used in the wave basin, making use of a Weibull-tail fitting procedure. The other is a novel method based on the level upcrossing function combined with an optimization procedure that allows prediction at extreme response levels. Similar results are obtained in the mean values by the two methods, while the latter shows less variability in the predictions from single 3 h records.