Oscillating point absorber buoys may rise out of the water and be subjected to bottom slamming upon re-entering the water. Numerical simulations are performed to estimate the power absorption, the impact velocities and the corresponding slamming forces for various slamming constraints. Three buoy shapes are considered: a hemisphere and two conical shapes with deadrise angles of 30° and 45°, with a waterline diameter of 5 m. The simulations indicate that the risk of rising out of the water is largely dependent on the buoy draft and sea state. Although associated with power losses, emergence occurrence probabilities can be significantly reduced by adapting the control parameters. The magnitude of the slamming load is severely influenced by the buoy shape. The ratio between the peak impact load on the hemisphere and that on the 45° cone is approximately 2, whereas the power absorption is only 4–8% higher for the 45° cone. This work illustrates the need to include slamming considerations aside from power absorption criteria in the buoy shape design process and the control strategy.