Extrapolating causal effects from experiments to novel populations is a common practice in evidence-based-policy, development economics and other social science areas. Drawing on experimental evidence of policy effectiveness, analysts aim to predict the effects of policies in new populations, which might differ importantly from experimental populations. Existing approaches made progress in articulating the sorts of similarities one needs to assume to enable such inferences. It is also recognized, however, that many of these assumptions will remain surrounded by significant uncertainty in practice. Unfortunately, the existing literature says little on how analysts may articulate and manage these uncertainties. This paper aims to make progress on these issues. First, it considers several existing ideas that bear on issues of uncertainty, elaborates the challenges they face, and extracts some useful rationales. Second, it outlines a novel approach, called the support graph approach, that builds on these rationales and allows analysts to articulate and manage uncertainty in extrapolation in a systematic and unified way.