We report the development of a mathematical model that quantifies the effects of small changes in systemic hematocrit (Hct) on the transport of nitric oxide (NO) in the microcirculation. The model consists of coupled transport equations for NO and oxygen (O2) and accounts for both shear-induced NO production by the endothelium and the effect of changing systemic Hct on the rate of NO production and the rate of NO scavenging by red blood cells. To incorporate the dependence of the plasma layer width on changes in Hct, the model couples the hemodynamics of blood in arterioles with NO and O2 transport in the plasma layer. A sensitivity analysis was conducted to determine the effects of uncertain model parameters (the thicknesses of endothelial surface layers and diffusion coefficients of NO and O2 in muscle tissues and vascular walls) on the model's predictions. Our analysis reveals that small increases in Hct may raise NO availability in the vascular wall. This finding sheds new light on the experimental data that show that the blood circulation responds to systematic increases of Hct in a manner that is consistent with increasing NO production followed by a plateau.