The function of the smooth muscle cells lining the walls of mammalian systemic arteries and arterioles is to regulate the diameter of the vessels to control blood flow and blood pressure. Here, we describe an in silico model, which we call the 'Hernandez-Hernandez model', of electrical and Ca2+ signaling in arterial myocytes based on new experimental data indicating sex-specific differences in male and female arterial myocytes from murine resistance arteries. The model suggests the fundamental ionic mechanisms underlying membrane potential and intracellular Ca2+ signaling during the development of myogenic tone in arterial blood vessels. Although experimental data suggest that KV1.5 channel currents have similar amplitudes, kinetics, and voltage dependencies in male and female myocytes, simulations suggest that the KV1.5 current is the dominant current regulating membrane potential in male myocytes. In female cells, which have larger KV2.1 channel expression and longer time constants for activation than male myocytes, predictions from simulated female myocytes suggest that KV2.1 plays a primary role in the control of membrane potential. Over the physiological range of membrane potentials, the gating of a small number of voltage-gated K+ channels and L-type Ca2+ channels are predicted to drive sex-specific differences in intracellular Ca2+ and excitability. We also show that in an idealized computational model of a vessel, female arterial smooth muscle exhibits heightened sensitivity to commonly used Ca2+ channel blockers compared to male. In summary, we present a new model framework to investigate the potential sex-specific impact of antihypertensive drugs.