Mechanically characterizing biological tissues at the microscale helps to better link microscale biomechanics to mechanobiology but also contributes to the mechanistic understanding of disease mechanobiology. Cell spheroids (CSs) are state-of-the-art in vitro three-dimensional cell cultures allowing for the synthesis of microtissue models into sphere-like geometry. Such a geometry is attractive for micromechanical assessment via parallel-plate compression, since only minimal and nondestructive sample preparation is required to conduct such tests. However, appropriate data analysis and interpretation methods are mostly lacking. Current approaches, relying on Hertzian theory and its modifications, are inadequate for capturing large deformations observed in CSs upon compression. Here, we utilized the extended Tatara model, incorporating hyperelasticity and nonlinear boundary effects, to investigate CS mechanics. To evaluate the effectiveness of the model, we compared results to Hertz, Ding, and simple Tatara models. The extended Tatara model demonstrated superior accuracy, enabling mechanical analysis of CSs under compression of up to 50% strain. Estimating the apparent Poisson's ratio via image segmentation and shape analysis helped refine the calculated apparent modulus. This work establishes a robust analytical framework that will, in the future, help advance our understanding of cardiac fibrosis progression and support the development of therapeutic strategies using patient-derived CSs as test models.