Ribbon-like magnetoelastic sensors vibrate at a characteristic frequency when excited by a time-varying magnetic field, with the resonance frequency and resonance amplitude dependent upon the viscosity of the surrounding medium. Hence when a magnetoelastic sensor is immersed within blood its resonance characteristics change with time due to blood clotting kinetics. An impedance analysis technique is applied to detect and analyze magnetoelastic sensor resonance characteristics, with which we have accurately determined the clotting time of heparin-doped bovine blood. The resulting highly compact system, with single-card electronics and a single miniature coil for sensor excitation and detection, coupled with the low material cost of the sensor result in a highly efficient and practical system for real-time characterization of blood clotting kinetics.