1. Human activities have led to widespread ecological decline; however, the severity of degradation is spatially heterogeneous due to some locations resisting, escaping, or rebounding from disturbances. 2. A framework is required to identify and characterise such locations, referred to here as "oases”, as they may have conservation value and can provide insight into mechanisms of resilience. We develop such a framework for identifying oases within coral-reef regions using long-term monitoring data. We calculated standardised estimates of coral cover (z-scores) to distinguish sites that deviated positively from regional means. We also used the coefficient of variation (CV) of coral cover to quantify how oases varied temporally and to distinguish among types of oases. To assess whether oases also had exceptional ecological function (e.g., calcification and reef construction), we estimated “coral calcification capacity” (CCC), a measure of the coral community’s ability to produce calcium carbonate structures and tested for an association between this metric and z-scores of coral cover. 4. We illustrate our z-score approach within a modelling framework by extracting z-scores and CVs from simulated data based on four generalized trajectories of coral cover. We then apply the approach to time-series data from long-term reef monitoring programs in four focal regions in the Pacific (the main Hawaiian Islands and Mo’orea, French Polynesia) and western Atlantic (the Florida Keys and St. John, US Virgin Islands). 5. Among the 123 sites analysed, 38 had positive z-scores for median coral cover and were categorised as oases. Thirty-two of these oases (84%) were temporally stable as defined by a CV ≤ 50%; in contrast, only two sites (5%) recovered from disturbances by increasing 74 coral cover. Z-scores for coral cover were positively associated with CCC, suggesting that our approach identified oases that are also exceptional for at least one measure of ecological function. Synthesis and applications. Identifying and characterizing coral-reef oases may provide a valuable tool for planning conservation and management strategies. Furthermore, evaluating the trajectories of change in coral cover among oases could allow researchers to identify the mechanisms responsible for spatial variability in reef condition and the controls on reef resilience.