Urban Building Energy Models (UBEMs) are emerging as a powerful tool for cities and regions seeking to make decisions on the best pathways for increasing the energy efficiency of their buildings. As model results are used to inform critical policy decisions, it is essential to understand and communicate the limits of inference of model results and how sensitive they are to changes in inputs. In the absence of standard datasets and protocols for model validation, Uncertainty Analysis and Sensitivity Analysis (UASA) procedures offer vital insights. However, there is no consensus on how UASA should be applied to bottom-up building physics-based UBEMs, nor on how different use cases might influence the choice of UASA approach. This study uses a systematic review of the literature (2009-2023) to explore the procedures which are applied and assess their appropriateness. We find a need for a more holistic view of uncertainty to be taken, and present a decision framework for selecting the most appropriate form of quantitative sensitivity analysis, based on model form, data provenance and use case. We also propose a number of approaches to improve the application of sensitivity analysis in UBEM studies, including the importance of undertaking a complementary assessment of information quality.