Understanding cell contractility is of fundamental importance for cardiovascular tissue engineering, due to its major impact on the tissue’s mechanical properties as well as the development of permanent dimensional changes, e.g., by contraction or dilatation of the tissue. Previous attempts to quantify contractile cellular stresses mostly used strongly aligned monolayers of cells, which might not represent the actual organization in engineered cardiovascular tissues such as heart valves. In the present study, therefore, we investigated whether differences in organization affect the magnitude of intrinsic stress generated by individual myofibroblasts, a frequently used cell source for in vitro engineered heart valves. Four different monolayer organizations were created via micro-contact printing of fibronectin lines on thin PDMS films, ranging from strongly anisotropic to isotropic. Thin film curvature, cell density, and actin stress fiber distribution were quantified, and subsequently, intrinsic stress and contractility of the monolayers were determined by incorporating these data into sample-specific finite element models. Our data indicate that the intrinsic stress exerted by the monolayers in each group correlates with cell density. Additionally, after normalizing for cell density and accounting for differences in alignment, no consistent differences in intrinsic contractility were found between the different monolayer organizations, suggesting that the intrinsic stress exerted by individual myofibroblasts is independent of the organization. Consequently, this study emphasizes the importance of choosing proper architectural properties for scaffolds in cardiovascular tissue engineering, as these directly affect the stresses in the tissue, which play a crucial role in both the functionality and remodeling of (engineered) cardiovascular tissues.