Electron cyclotron resonance heating (ECRH) and electron cyclotron current drive systems in fusion-grade devices meet the severe requirements (in terms of high power handling capability, extended steering range, and room availability) that guide the design of complex multiple-mirror quasi-optical launchers. A valuable step in this process is a beam-pattern calculation in vacuum including relevant electromagnetic effects not easily included in analytical evaluations. In fact, the analytical approach is a means to study the design layout at a first order and is able to derive the relevant quantities as a function of the steering angle and of the beam path in a form suitable to interface with most of the currently available beam-tracing codes. On the other hand, electromagnetic calculations using physical optics tools provide a complete description of the resulting full beam pattern, including the effects of aberration, beam truncation, thermal deformation of the mirrors, and the surrounding structures. Moreover, numerical calculation with reliable and benchmarked codes is a very efficient way to test subsequent updates of a given launcher model, once the basic geometry has been implemented. In this paper, we discuss in particular the application of the GRASP® code to the case of the remote steering option for the ITER ECRH upper launcher.