The supported bilayer is an important experimental method for probing the features of lipid bilayers, yet relatively few computational studies have taken up its modeling. Using coarse-grained molecular dynamics simulations based on the MARTINI force field, we show that some of the few previous attempts employing similar methodologies are problematic, and have indeed led to erroneous conclusions. We further build a theoretical framework to see where exactly the failures of parametrization lie and suggest how these earlier results should be interpreted. The lessons learned may also prove useful in areas other than the supported bilayer as there is a current trend in modifying MARTINI, and other force fields, to suit a wide variety of specific applications. Finally, we analyze the polarizable water version of MARTINI and, although finding it imperfect in some of the same regards as the standard MARTINI, suggest using it in conjunction with supported bilayers.