Well-controlled 2D cell culture systems advance basic investigations in cell biology and provide innovative platforms for drug development, toxicity testing, and diagnostic assays. These cell culture systems have become more advanced in order to provide and to quantify the appropriate biomechanical and biochemical cues that mimic the milieu of conditions present in vivo. Here we present an innovative 2D cell culture system to investigate human stem cell-derived cardiomyocytes, the muscle cells of the heart responsible for pumping blood throughout the body. We designed our 2D cell culture platform to control intracellular features to produce adult-like cardiomyocyte organization with connectivity and anisotropic conduction comparable to the native heart, and combined it with optical microscopy to quantify cell-cell and cell-substrate mechanical interactions. We show the measurement of forces and displacements that occur within individual cells, between neighboring cells, and between cells and their surrounding matrix. This system has broad potential to expand our understanding of tissue physiology, with particular advantages for the study of the mechanically active heart. Furthermore, this technique should prove valuable in screening potential drugs for efficacy and testing for toxicity.