Solidification Microstructure Selection (SMS) maps provide a simple yet effective approach to predict the non-equilibrium solidification microstructure and grain morphology during Additive Manufacturing. In this study, SMS maps have been created for the Inconel 625 (IN625) alloy processed by Laser Powder Bed Fusion (LPBF). Toward this end, theoretical solid growth models, a model of the Columnar to Equiaxed Transition (CET), interface response theory, thermal simulation results and computational thermodynamics are utilized. The predicted microstructures are compared both qualitatively and quantitatively to experimentally-obtained micrographs. The theoretical analysis was also compared to the earlier analytical calculation for Al-10Si-0.5Mg alloy to show how differences in thermophysical properties affect the microstructural predictions. The theoretical predictions are shown to be in good agreement with the experimental results in terms of the resulting microstructure and dendrite arm spacings. A discussion on the use of SMS maps, formed over a broad range of thermophysical conditions, to help guide industry in improving LPBF microstructure, is provided.