In quantitative micro-elastography (QME), a pre-characterized compliant layer with a known stress-strain curve is utilized to map stress at the sample surface. However, differences in the boundary conditions of the compliant layer when it is mechanically characterized and when it is used in QME experiments lead to inconsistent stress estimation and consequently, inaccurate elasticity measurements. Here, we propose a novel in situ stress estimation method using an optical coherence tomography (OCT)-based uniaxial compression testing system integrated with the QME experimental setup. By combining OCT-measured axial strain with axial stress determined using a load cell in the QME experiments, we can estimate in situ stress for the compliant layer, more accurately considering its boundary conditions. Our proposed method shows improved accuracy, with an error below 10%, compared to 85% using the existing QME technique with no lubrication. Furthermore, demonstrations on hydrogels and cells indicate the potential of this approach for improving the characterization of the micro-scale mechanical properties of cells and their interactions with the surrounding biomaterial, which has potential for application in cell mechanobiology.