The meshless radial point interpolation method (RPIM) in frequency domain for electromagnetic scattering problems is presented. This method promises high accuracy in a simple collocation approach using radial basis functions. The treatment of high-order non-reflecting boundary conditions for open waveguides is discussed and implemented up to fourth-order. RPIM allows the direct calculation of high-order spatial derivatives without the introduction of auxiliary variables. High-order absorbing boundary conditions offer a choice of absorbing angles for each degree of spatial derivatives. For general applications, a set of these absorbing angles is calculated using global optimization. Numerical experiments show that at the same computational cost, the numerical reflections of the absorbing boundary conditions are much lower than conventional perfectly matched layers, especially at high angles of incidence. Copyright © 2013 John Wiley & Sons, Ltd.