We quantitatively evaluate the fidelity with which the Northern Annular Mode (NAM), Southern Annular Mode (SAM), Pacific-North American pattern (PNA), El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO) and Atlantic Multidecadal Oscillation (AMO) and their first-order interactions are represented in Earth System Model (ESM) output from the CMIP6 archive. Several skill metrics are used as part of a differential credibility assessment (DCA) of both spatial and temporal characteristics of the modes across ESMs, ESM families and specific ESM realizations relative to ERA5. The spatial patterns and probability distributions are generally well represented, however frequencies of maximum variance score consistently lower for most ESMs and climate modes. Substantial variability in skill scores manifests across realizations from individual ESMs for the PNA and oceanic modes. Interactions between modes centered in the Pacific tend to be better represented than interactions between modes centered in different regions, with ESMs consistently overestimating the strength of the NAM-PNA interaction and underestimate the NAM-AMO connection. Finally, we compare changes in mode characteristics under future warming scenarios (SSP 2.6 and SSP 8.5) for ‘good’, ‘moderate’ and ‘poor’ ESM representations of the modes in the current climate. Our research can provide guidance regarding which ESM(s) and ESM realization(s) have highest credibility in terms of global and regional climate projections.