It is now possible to collect and share trajectory data for any ship in the world by various means such as satellite and VHF systems. However, the publication of such data also creates new risks for privacy breach with consequences on the security and liability of the stakeholders. Thus, there is an urgent need to develop methods for preserving the privacy of published trajectory data. In this paper, we propose and comparatively investigate two mechanisms for the publication of the trajectory of individual ships under differential privacy guarantees. Traditionally, privacy and differential privacy is achieved by perturbation of the result or the data according to the sensitivity of the query. Our approach, instead, combines sampling and interpolation. We present and compare two techniques in which we sample and interpolate (a priori) and interpolate and sample (a posteriori), respectively. We show that both techniques achieve a (0,
) form of differential privacy. We analytically and empirically, with real ship trajectories, study the privacy guarantee and utility of the methods.