The amount of coronary artery calcification (CAC) is a strong and independent predictor of cardiovascular events. We present a system that automatically quantifies total patient and per coronary artery CAC in non-contrast-enhanced, ECG-triggered cardiac CT. The system identifies candidate calcifications that cannot be automatically labeled with high certainty and optionally presents these to an expert for review. Candidates were extracted by intensity-based thresholding and described by location features derived from estimated coronary artery positions, as well as size, shape and intensity features. Next, a two-class classifier distinguished between coronary calcifications and negatives or a multiclass classifier labeled CAC per coronary artery. Candidates that could not be labeled with high certainty were identified by entropy-based ambiguity detection and presented to an expert for review and possible relabeling. The system was evaluated with 530 test images. Using the two-class classifier, the intra-class correlation coefficient (ICC) between reference and automatically determined total patient CAC volume was 0.95. Using the multiclass classifier, the ICC between reference and automatically determined per artery CAC volume was 0.98 (LAD), 0.69 (LCX), and 0.95 (RCA). In 49% of CTs, no ambiguous candidates were identified, while review of the remaining CTs increased the ICC for total patient CAC volume to 1.00, and per artery CAC volume to 1.00 (LAD), 0.95 (LCX), and 0.99 (RCA). In conclusion, CAC can be automatically identified in non-contrast-enhanced ECG-triggered cardiac CT. Ambiguity detection with expert review may enable the application of automatic CAC scoring in the clinic with a performance comparable to that of a human expert.