We propose a CFD-based approach for the non-invasive hemodynamic assessment of pre- and post-operative coarctation of aorta (CoA) patients. Under our approach, the pressure gradient across the coarctation is determined from computational modeling based on physiological principles, medical imaging data, and routine non-invasive clinical measurements. The main constituents of our approach are a reduced-order model for computing blood flow in patient-specific aortic geometries, a parameter estimation procedure for determining patient-specific boundary conditions and vessel wall parameters from non-invasive measurements, and a comprehensive pressure-drop formulation coupled with the overall reduced-order model. The proposed CFD-based algorithm is fully automatic, requiring no iterative tuning procedures for matching the computed results to observed patient data, and requires approximately 6-8 min of computation time on a standard personal computer (Intel Core2 Duo CPU, 3.06 GHz), thus making it feasible for use in a clinical setting. The initial validation studies for the pressure-drop computations have been performed on four patient datasets with native or recurrent coarctation, by comparing the results with the invasively measured peak pressure gradients recorded during routine cardiac catheterization procedure. The preliminary results are promising, with a mean absolute error of less than 2 mmHg in all the patients.