Macrophages from animals prone to autoimmune (type 1) diabetes differ from those of diabetes-resistant animals in processing and clearing apoptotic cells. Using in vitro time-course assays of the number of engulfed apoptotic cells observed within macrophages, we quantified these differences in non-obese diabetic (NOD) versus Balb/c mice. Simple models lead to several elementary parameter estimation techniques. We used these to compute approximate rates of macrophage engulfment and digestion of apoptotic cells from basic features of the data (such as initial rise-times, phagocytic index and percent phagocytosis). Combining these estimates with full fitting of a sequence of model variants to the data, we find that macrophages from normal (Balb/c) mice engulf apoptotic cells up to four times faster than macrophages from the diabetes-prone (NOD) mice. Further, Balb/c macrophages appear to undergo an activation step before achieving their high engulfment rate. In NOD macrophages, we did not see evidence for this activation step. Rates of digestion of engulfed apoptotic cells by macrophages are similar in both types. Since macrophage clearance is an important mechanism of disposal of self-antigen, these macrophage defects could potentially be a factor in predisposition to type 1 diabetes.