We present a novel multi-resolution variational framework for vascular optical coherence elastography (OCE). This method exploits prior information about arterial wall biomechanics to produce robust estimates of tissue velocity and strain, reducing the sensitivity of conventional tracking methods to both noise- and strain-induced signal decorrelation. The velocity and strain estimation performance of this new estimator is demonstrated in simulated OCT image sequences and in benchtop OCT scanning of a vascular tissue sample.