The aviation industry and policymakers are advocating Sustainable Aviation Fuels (SAF) as one of the main pillars for making the aviation industry sustainable. However, regulatory frameworks like CORSIA and the EU Renewable Energy Directive often exclude the climate impact from in-flight non-CO2 emissions (e.g., NOx, H2O, and soot emissions), which is important in determining the effect of SAF in reducing the climate impact of aviation. To bridge this gap, we evaluate the total global warming effects of SAF from a well-to-wake analysis, which includes the climate effects from CO2 emissions of the well-to-wake combined with the non-CO2 emissions of the pump-to-wake (i.e., inflight). We quantify the climate impact of NOx, H2O and contrails and convert them to a CO2 equivalence (CO2e) factor based on a climate metric, for instance, the Average Temperature Response over a given time horizon (i.e., 20, 50 and 100 years). The resulting well-to-wake CO2e values for SAF vary from about 150 to 250 g/MJ, depending on the specific fuel pathways. Our analysis shows that the maximum reduction in CO2e emissions when using SAF is less than 50% compared to conventional jet fuel, mainly due to the inflight NOx and contrail effects.