In this work, a novel Boundary Element Method (BEM) is developed and applied to the investigation of the performance of Oscillating Water Column (OWC) systems, taking into account the interaction of the incident wave field with the bottom topography. The modelling includes the effect of additional upwave walls and barriers used to modify the resonance characteristics of the device and improve its performance as the U-OWC configuration. Numerical results illustrating the effects of depth variation in conjunction with other parameters—such as chamber dimensions as well as the parameters associated with the turbine and power take-off system—on the device performance are presented and discussed. Finally, a case study is presented regarding the potential installation of an OWC in a selected port site in the Black Sea, characterized by a good wave energy potential, on the coast of Romania.