This paper introduces a system designed for tight collaboration between Unmanned Aerial Vehicles (UAVs) and Unmanned Surface Vehicles (USVs) in harsh maritime conditions characterized by large waves. This onboard UAV system aims to enhance collaboration with USVs for following and landing tasks under such challenging conditions. The main contribution of our system is the novel mathematical USV model, describing the movement of the USV in 6 degrees of freedom on a wavy water surface, which is used to estimate and predict USV states. The estimator fuses data from multiple global and onboard sensors, ensuring accurate USV state estimation. The predictor computes future USV states using the novel mathematical USV model and the last estimated states. The estimated and predicted USV states are forwarded into a trajectory planner that generates a UAV trajectory for following the USV or landing on its deck, even in harsh environmental conditions. The proposed approach was verified in numerous simulations and deployed to the real world, where the UAV was able to follow the USV and land on its deck repeatedly.