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Abstract: Objective: Optical coherence elastography (OCE) allows for high resolution analysis of elastic tissue properties. However, due to the limited penetration of light into tissue, miniature probes are required to reach structures inside the body, e.g., vessel walls. Shear wave elastography relates shear wave velocities to quantitative estimates of elasticity. Generally, this is achieved by measuring the runtime of waves between two or multiple points. For miniature probes, optical fibers have been integrated and the runtime between the point of excitation and a single measurement point has been considered. This approach requires precise temporal synchronization and spatial calibration between excitation and imaging. Methods: We present a miniaturized dual-fiber OCE probe of $1 \,\mathrm{m}\mathrm{m}$ diameter allowing for robust shear wave elastography. Shear wave velocity is estimated between two optics and hence independent of wave propagation between excitation and imaging. We quantify the wave propagation by evaluating either a single or two measurement points. Particularly, we compare both approaches to ultrasound elastography. Results: Our experimental results demonstrate that quantification of local tissue elasticities is feasible. For homogeneous soft tissue phantoms, we obtain mean deviations of $0.15 \,\mathrm{m}\mathrm{s}^{-1}$ and $0.02 \,\mathrm{m}\mathrm{s}^{-1}$ for single-fiber and dual-fiber OCE, respectively. In inhomogeneous phantoms, we measure mean deviations of up to $0.54 \,\mathrm{m}\mathrm{s}^{-1}$ and $0.03 \,\mathrm{m}\mathrm{s}^{-1}$ for single-fiber and dual-fiber OCE, respectively. Conclusion: We present a dual-fiber OCE approach that is much more robust in inhomogeneous tissues. Moreover, we demonstrate the feasibility of elasticity quantification in ex-vivo coronary arteries. Significance: This study introduces an approach for robust elasticity quantification from within the tissue.