Coronal holes (CH) are dark areas in EUV images that are generally associated with open magnetic field regions on the Sun. They can be used to estimate the open magnetic flux in the heliosphere by overlaying them on magnetic field measurements. Accurately measuring the CH boundaries over the whole Sun remains challenging due to many factors, including limited instrument coverage, obstruction by nearby bright structures, and the assumptions of a given detection algorithm. Here we explore the effects of CH obscuration using a global thermodynamic MHD model of the corona. We generate synthetic EUV images for several sets of observer locations, and combine them into maps using current and new obscuration-mitigating strategies. CH maps are generated from each resulting EUV map (using an established CH detection algorithm) and used to estimate the open flux. The importance of synchronizing the effective EUV image height to the height of the magnetic field values is demonstrated. Comparisons of the CH contours and open flux results with the known open field in the simulation gives insight into how much CH obscuration might influence observationally detected CH maps and open flux estimates. Application of obscuration-mitigating mapping techniques to observations is also discussed.