The Heterodyne Instrument for the Far-Infrared (HIFI) of the ESA cornerstone mission Herschel is required to operate at wavelengths between 157 and 625 Î¼m. Because of the long-wavelength character, and the complexity and modularity of the optical design, there is a clear need for accurate electromagnetic simulations supported by experimental verification. The need for a compact layout in order to reduce mass and volume as far as possible has important optical consequences. Several mirrors are illuminated in the propagating near-field rather than in the far-field. Consequently the classical geometrical design and analysis approach is inadequate. The long-wavelength character of the system can not be ignored and the associated diffraction effects inevitably become important. In this paper we describe the results of electromagnetic simulations of the optical system for band 1 of HIFI at a wavelength of 625 Î¼m. In order to verify the results of the front-to-end coherent propagation of the detector beams, near-field facilities capable of measuring both amplitude and phase of the electromagnetic field have been developed. A unique feature of these facilities is that the absolute coordinates of the measured field components are known within a fraction of a wavelength. Therefore a true comparison with theoretical predictions can be made. We compare measurement data taken at 625 Î¼m with simulations and discuss to what extent measured and simulated results may be expected to agree. We conclude by presenting the consequences of our observations in terms of system performance.