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We discuss the use of wavelets in the method of moments solution to integral equations arising in two typical electromagnetic problems. In the first problem, we analyse the arbitrarily shaped patch antenna with resistive wall boundary, formulated as a boundary element method problem using a contour integral. In the second problem, three-dimensional electromagnetic scattering from a large flat conducting plate is studied. The problem is formulated as an EFIE and discretized with Rao-Wilton-Glisson (RWG) vector basis functions.