The immature physiology of cardiomyocytes derived from human induced pluripotent stem cells (hiPSCs) limits their utility for drug screening and disease modelling. Here we show that suitable combinations of mechanical stimuli and metabolic cues can enhance the maturation of hiPSC-derived cardiomyocytes, and that the maturation-inducing cues have phenotype-dependent effects on the cells' action-potential morphology and calcium handling. By using microfluidic chips that enhanced the alignment and extracellular-matrix production of cardiac microtissues derived from genetically distinct sources of hiPSC-derived cardiomyocytes, we identified fatty-acid-enriched maturation media that improved the cells' mitochondrial structure and calcium handling, and observed divergent cell-source-dependent effects on action-potential duration (APD). Specifically, in the presence of maturation media, tissues with abnormally prolonged APDs exhibited shorter APDs, and tissues with aberrantly short APDs displayed prolonged APDs. Regardless of cell source, tissue maturation reduced variabilities in spontaneous beat rate and in APD, and led to converging cell phenotypes (with APDs within the 300-450 ms range characteristic of human left ventricular cardiomyocytes) that improved the modelling of the effects of pro-arrhythmic drugs on cardiac tissue.