Several studies have projected increases in drought severity, extent and duration in many parts of the world under climate change. We examine sources of uncertainty arising from the methodological choices for the assessment of future drought risk in the continental US (CONUS). One such uncertainty is in the climate models' expression of evaporative demand (E0), which is not a direct climate model output but has been traditionally estimated using several different formulations. Here we analyze daily output from two CMIP5 GCMs to evaluate how differences in E0 formulation, treatment of meteorological driving data, choice of GCM, and standardization of time series influence the estimation of E0. These methodological choices yield different assessments of spatio-temporal variability in E0 and different trends in 21st century drought risk. First, we estimate E0 using three widely used E0 formulations: Penman-Monteith; Hargreaves-Samani; and Priestley-Taylor. Our analysis, which primarily focuses on the May-September warm-season period, shows that E0 climatology and its spatial pattern differ substantially between these three formulations. Overall, we find higher magnitudes of E0 and its interannual variability using Penman-Monteith, in particular for regions like the Great Plains and southwestern US where E0 is strongly influenced by variations in wind and relative humidity. When examining projected changes in E0 during the 21st century, there are also large differences among the three formulations, particularly the Penman-Monteith relative to the other two formulations. The 21st century E0 trends, particularly in percent change and standardized anomalies of E0, are found to be sensitive to the long-term mean value and the amplitude of interannual variability, i.e. if the magnitude of E0 and its interannual variability are relatively low for a particular E0 formulation, then the normalized or standardized 21st century trend based on that formulation is amplified relative to other formulations. This is the case for the use of Hargreaves-Samani and Priestley-Taylor, where future E0 trends are comparatively much larger than for Penman-Monteith. When comparing Penman-Monteith E0 responses between different choices of input variables related to wind speed, surface roughness, and net radiation, we found differences in E0 trends, although these choices had a much smaller influence on E0 trends than did the E0 formulation choices. These methodological choices and specific climate model selection, also have a large influence on the estimation of trends in standardized drought indices used for drought assessment operationally. We find that standardization tends to amplify divergences between the E0 trends calculated using different E0 formulations, because standardization is sensitive to both the climatology and amplitude of interannual variability of E0. For different methodological choices and GCM output considered in estimating E0, we examine potential sources of uncertainty in 21st century trends in the Standardized Precipitation Evapotranspiration Index (SPEI) and Evaporative Demand Drought Index (EDDI) over selected regions of the CONUS to demonstrate the practical implications of these methodological choices for the quantification of drought risk under climate change.