Wave energy converters (WECs) are a promising technology aimed at harvesting energy by converting the device motion induced by ocean and sea waves. The control strategy adopted to guide the power take-off (PTO) system is among the most crucial aspects in the energy conversion process. Indeed, the solution of such an energy-maximizing optimal control problem is fundamental for the economic viability of this type of emerging technology. State-of-the-art WEC control technology can be almost fully enclosed within the family of model-based control strategies: The optimal control law, which maximizes energy absorption, is computed based upon knowledge of a dynamical model of the device, able to predict the associated motion. Nonetheless, models constructed for WEC control purposes are inherently affected by several sources of uncertainty, especially in terms of the associated hydrodynamic effects. As a consequence, there is a significant appetite to adopt model-free control strategies to overcome this issue. In this study, we propose a perturbation-based extremum-seeking control (ESC) in which a class of soft-constraint handling has been introduced to deal with excessive motion values for a heaving point absorber WEC. We test such a strategy in different operating conditions to highlight the influence of the soft constraint mechanism on power absorption, applied control action, and WEC velocity.