A common problem with global climate models is the fact that their grids do not always resolve important topographic features which determine the spatial variability of rainfall at regional scales. Here we present and compare simulations of rainfall for the relatively mountainous New Guinea region from six relatively coarse resolution climate models and the corresponding results using a higher resolution model (the Conformal Cubic Atmospheric Model—CCAM). While the large-scale climatological mean rainfall from both the coarse models and CCAM tend to be similar, unsurprisingly, the CCAM results better reflect some of the important topographic effects. However, the results for projected changes (under the A2 emissions scenario) to rainfall for later this century reveal some important differences. The coarse-scale results indicate relatively smooth patterns of projected change consistent with the representations of the underlying topography, but over New Guinea, there is little agreement on the sign of the change. The CCAM projections show greater spatial detail and better agreement among the six members. These indicate that West Papua and the relatively wet northern and southern mountain slopes may get wetter during December to February—the peak of the Austral monsoon season, and the highland regions may actually become drier during June to August—the dry season. These results are consistent with the theoretical concept that warmer temperatures may lead to increases over already wet regions and decreases over the relatively drier regions—the so-called “rich-get-richer” mechanism. They also highlight the fact that the climate of mountainous regions can be relatively complex and indicate potential difficulties that can arise when attempting to synthesize regional-scale projections from coarse-scale models.