Determining a precise local geoid is particularly important for converting the Global Navigation Satellite System (GNSS) heights to orthometric heights. The geometric method for computing the geoid has been extensively used for a comparatively small region, which, in some points, interpolates geoid heights based on GNSS-derived heights and levelling heights. Several considerations should be considered when using the geometric method to increase the accuracy of a local geoid. Kuwait is used as a test area in this paper to investigate several features of the geometric method. The achievable precision is one of these aspects, the role of the interpolation method, global geopotential models, and the influence of the topographic effect. The accuracy of the local geoid can be substantially enhanced by integrating a geopotential model with a digital terrain model of the research region. It is possible to get a precision of 2–3 cm