Numerical methods are employed in the preliminary stages of spacecraft trajectory design, due to the accessibility of the underlying theory and relative ease of implementation. While having a more complex theoretical basis, semi-analytical methods can provide intuitive insights lost to mission designers who only consider present numerical procedures. These techniques are complementary yet have developed separately over the past few decades. Hence, their unified use requires new strategies. Taking as case studies the autonomous and non-autonomous models of cislunar space, we perform separately studies using semi-analytical and numerical methods. In particular, we develop and analyze local orbital elements, a local analog in the circular restricted 3-body problem to the classical orbital elements of the two-body problem. Additionally, we provide two in-depth investigations on regions of cislunar space in a higher-fidelity model of the Sun-Earth-Moon system. Throughout this thesis, we discuss connections between such methods, and we show explicitly the collaboration between semi-analytical and numerical techniques to compute particular quasi-periodic orbits in the Sun-Earth-Moon system. Overall, the presented work seeks to integrate semi-analytical methods into the standard numerical methodology for preliminary mission design.