The coupling of partial differential equations across subdomains has proven advantageous in various disciplines, including hematology, aerodynamics and hydraulics. The advantages are multiple: increased computational efficiency, robustness, improved qualitative properties, etc. In coastal oceanography, coupled shallow water wave models have been successfully employed since the 1990s, demonstrating remarkable accuracy even for complex phenomena like wave breaking and inundation. Despite this success, a debate exists in the literature regarding oscillations that, sometimes, completely spoiled the computations. Despite efforts to analyze these oscillations, a precise mathematical explanation has remained elusive. In this talk I will present the work of my PhD, which introduces a novel mathematical framework for analyzing such coupled systems. This method is based on the notions of reflections and weak well-posedness of wave models. This allows us to explain precisely when the “price to pay” (oscillations) with such systems is minimal, while making explicit some conditions that are necessary for the stability of numerical methods, which may explain many of the reported issues from the literature.