In hematologic diseases, such as sickle cell disease (SCD) and hemolytic uremic syndrome (HUS), pathological biophysical interactions among blood cells, endothelial cells, and soluble factors lead to microvascular occlusion and thrombosis. Here, we report an in vitro "endothelialized" microfluidic microvasculature model that recapitulates and integrates this ensemble of pathophysiological processes. Under controlled flow conditions, the model enabled quantitative investigation of how biophysical alterations in hematologic disease collectively lead to microvascular occlusion and thrombosis. Using blood samples from patients with SCD, we investigated how the drug hydroxyurea quantitatively affects microvascular obstruction in SCD, an unresolved issue pivotal to understanding its clinical efficacy in such patients. In addition, we demonstrated that our microsystem can function as an in vitro model of HUS and showed that shear stress influences microvascular thrombosis/obstruction and the efficacy of the drug eptifibatide, which decreases platelet aggregation, in the context of HUS. These experiments establish the versatility and clinical relevance of our microvasculature-on-a-chip model as a biophysical assay of hematologic pathophysiology as well as a drug discovery platform.