Climate science is increasingly using (i) ensembles of climate projections from multiple models derived using different assumptions and/or scenarios and (ii) process-oriented diagnostics of model fidelity. Efforts to assign differential credibility to projections and/or models are also rapidly advancing. A framework to quantify and depict the credibility of statistically downscaled model output is presented and demonstrated. The approach employs transfer functions in the form of robust and resilient generalized linear models applied to downscale daily minimum and maximum temperature anomalies at 10 locations using predictors drawn from ERA-Interim reanalysis and two global climate models (GCM; GFDL-ESM2M and MPI-ESM-LR). The downscaled time series are used to derive several impact-relevant Climate Extreme (CLIMDEX) temperature indices that are assigned credibility based on 1) the reproduction of relevant large-scale predictors by the GCMs (i.e., fraction of regression beta weights derived from predictors that are well reproduced) and 2) the degree of variance in the observations reproduced in the downscaled series following application of a new variance inflation technique. Credibility of the downscaled predictands varies across locations and between the two GCM and is generally higher for minimum temperature than for maximum temperature. The differential credibility assessment framework demonstrated here is easy to use and flexible. It can be applied as is to inform decision-makers about projection confidence and/or can be extended to include other components of the transfer functions, and/or used to weight members of a statistically downscaled ensemble.