Atmospheric pCO2 is predicted to rise from 400 to 900 ppm by year 2100, causing seawater temperature to increase by 1-4 °C and pH to decrease by 0.1-0.3. Sixty-day experiments were conducted to investigate the independent and combined impacts of acidification (pCO2 = 424-426, 888-940 ppm-v) and warming (T = 28, 32 °C) on calcification rate and skeletal morphology of the abundant and widespread Caribbean reef-building scleractinian coral Siderastrea siderea. Hierarchical linear mixed-effects modelling reveals that coral calcification rate was negatively impacted by both warming and acidification, with their combined effects yielding the most deleterious impact. Negative effects of warming (32 °C/424 ppm-v) and high-temperature acidification (32 °C/940 ppm-v) on calcification rate were apparent across both 30-day intervals of the experiment, while effects of low-temperature acidification (28 °C/888 ppm-v) were not apparent until the second 30-day interval-indicating delayed onset of acidification effects at lower temperatures. Notably, two measures of coral skeletal morphology-corallite height and corallite infilling-were negatively impacted by next-century acidification, but not by next-century warming. Therefore, while next-century ocean acidification and warming will reduce the rate at which corals build their skeletons, next-century acidification will also modify the morphology and, potentially, function of coral skeletons.