Human-induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) are increasingly important in preclinical drug assessments, particularly for identifying potential cardiotoxicity. In this study, we utilize data from microphysiological systems of hiPSC-CMs to evaluate cellular characteristics, such as action potential duration, beat rate, conduction velocity and mechanical displacement. Based on these data, high-fidelity mathematical models facilitate precise assessments of critical biophysical parameters of the cells, including membrane ion channel conductances, cross-bridge cycle transition rates and cell-to-cell conductance. We emphasize the distinction between synchronized transients and travelling waves, highlighting their implications for deducing the biophysical properties of hiPSC-CMs. In this study, we analyse the effects of the drug compounds flecainide, quinidine, nifedipine, verapamil, blebbistatin and omecamtiv. Our findings show that for drug-induced changes in parameters describing membrane currents and contractile machinery close to ranges reported in the literature, the computed biomarkers align well with measured biomarkers. This study is the first to apply spatially resolved, cell-based models to identify drug effects through measurements of transmembrane potential and mechanical displacement, marking a significant step forward in using computational models for evaluating drug safety and offering a new approach to early identification of adverse drug reactions. KEY POINTS: Optical measurements of human-induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) present significant opportunities to advance understanding of how human heart cells function and interact. Although direct optical measurements yield valuable biomarkers, they fall short of revealing underlying biophysical properties, for example, how novel drug compounds perturb the ion channels. Drug properties are best understood through computational models that capture cell dynamics based on physical laws. Traditionally, data and models have been averaged over all cells in cell collections, thus overlooking spatiotemporal waves. Here, we use recently developed cell-based models, representing spatial dynamics including cell-to-cell electrical and mechanical coupling, to determine biophysical properties of collections of hiPSC-CMs.