Microwaves have been shown to be able to detect surface breaking hairline cracks on metal specimens [1]. A microwave signal is typically fed through a rectangular waveguide probe. The incident and reflected signals in the waveguide form a standing wave, whose characteristics change depending on the relative position of a crack and the rectangular waveguide probe. Two separate electromagnetic models have been developed to mathematically predict the crack characteristic signal, i.e. the variation of the measured standing wave in the waveguide when it is scanned across a surface breaking crack. These models can be used to optimize measurement parameters. One model uses a mode matching approach, whereas the other model involves a moment solution approach. This paper presents a comparision of these two methodologies, which demonstrates the major advantages in the use of a moment solution approach. The most important result shown is that a moment solution approach is more general, eliminating the destinction between a crack being at the edge or in the middle of a rectangular waveguide probe. The convergence behavior is also studied for both methodologies. Faster convergence is observed using the moment solution approach. Finally, a moment solution approach allows for an easy expansion of the electromagnetic model to the analysis of finite cracks, and can be more readily expanded to encompass covered cracks as well.