In this work, we examine the methodology for numerically computing the dispersion diagram of three-dimensional periodic structures using commercial electromagnetic simulators. Examples of periodic structures based on body-centered cubic, face-centered cubic, and monoclinic lattices are used to illustrate this methodology. We first outline the characteristics of these structures in both physical and reciprocal spaces from a theoretical point of view. On this basis, we provide a comprehensive explanation of how to adjust the setting in simulation software commonly used in microwave engineering to generate the dispersion diagrams of these structures. The appropriate simulation conditions are tabulated to serve as a further guide for other researchers. This study also explores the influence of the elements of the unit cell on the dispersion characteristics. Additionally, we evaluate and contrast the dispersion properties of identical periodic elements when having simple cubic, body-centered cubic, and face-centered cubic arrangements. We found that symmetries, such as those seen in body-centered cubic and face-centered cubic arrangements, can improve the isotropy and maintain low-dispersion characteristics over a wider frequency range. The monoclinic structure is also taken as an example to demonstrate that the reported analysis method can be applied to the dispersion analysis of other more complex noncubic lattices. Our findings offer useful information for the examination and engineering of three-dimensional periodic structures, which can be used to design microwave and antenna devices.