Abstract. Boundary Integral Equation formulations can be used to describe electromagnetic shielding problems. Yet, this approach frequently leads to integrals which contain a singularity and an oscillating part. Those integrals are difficult to handle when integrated naivly using standard integration techniques, and in some cases even a very high number of integration nodes will not lead to precise results. We present a method for the numerical quadrature of an integral with a logarithmic singularity and a cosine oscillator: a modified Filon-Lobatto quadrature for the oscillating parts and an integral transformation based on the error function for the singularity. Since this integral can be solved analytically, we are in a position to verify the results of our investigations, with a focus on precision and computation time.