We discuss a mesh-based Trefftz method for approximating time harmonic electromagnetic wave propagation using the Ultra Weak Variational Formulation (UWVF) discretized using plane waves. We review some history of this method, as well as mentioning several interesting current directions of research. Our focus is on approximating solutions of Maxwell’s equations near piecewise smooth curved boundaries or interfaces. Numerical examples, including the approximation of the Radar Cross Section for an almond shaped scatterer, demonstrate the methodology’s effectiveness. The results indicate that UWVF can efficiently approximate solutions for complex scatterers with singularities, offering a flexible and scalable alternative to traditional finite element methods.