Contemporaneous occurrences of extreme seas at multiple locations in a neighbourhood can cause greater structural reliability and human safety concerns than extremes at a single location. Understanding spatial dependence of extreme seas is important therefore in metocean design, yet has received little rigorous attention in the offshore engineering literature. We characterise the spatial dependence of storm peak significant wave height using three models motivated by max-stable processes for locations in the northern North Sea. Models for marginal extremes per location, and dependence of extremes between locations, are estimated using Bayesian inference with composite spatial likelihoods. We show that, in addition to marginal directional non-stationarity of extreme seas per location, all three models indicate spatial anisotropy in extremal dependence quantified by the spatial covariance matrix of the corresponding max-stable process. Estimates suggest that extreme seas show greater extremal dependence from West to East than from North to South.