We assess internally-generated climate variability expressed by a multi-model ensemble of unperturbed climate simulations. We focus on basin-scale annual-average sea surface temperatures (SSTs) from twenty multicentennial pre-industrial control simulations contributing to the fifth phase of the Coupled Model Intercomparison Project. Ensemble spatial patterns of regional modes of variability and ensemble (cross-)wavelet-based phase-frequency diagrams of corresponding paired indices summarize the ensemble characteristics of inter-basin and regional-to-global SST interactions on a broad range of timescales. Results reveal that tropical and North Pacific SSTs are a source of simulated interannual global SST variability. The North Atlantic-average SST fluctuates in rough co-phase with the global-average SST on multidecadal timescales, which makes it difficult to discern the Atlantic Multidecadal Variability (AMV) signal from the global signal. The two leading modes of tropical and North Pacific SST variability converge towards co-phase in the multi-model ensemble, indicating that the Pacific Decadal Oscillation (PDO) results from a combination of tropical and extra-tropical processes. No robust inter- or multi-decadal inter-basin SST interaction arises from our ensemble analysis between the Pacific and Atlantic oceans, though specific phase-locked fluctuations occur between Pacific and Atlantic modes of SST variability in individual simulations and/or periods within individual simulations. The multidecadal modulation of PDO by the AMV identified in observations appears to be a recurrent but not typical feature of ensemble-simulated internal variability. Understanding the mechanism(s) and circumstances favoring such inter-basin SST phasing and related uncertainties in their simulated representation could help constraining uncertainty in decadal climate predictions.