Tissue-engineered grafts may be useful in myocardial repair; however, previous scaffolds have been structurally incompatible with recapitulating cardiac anisotropy. Here, we use microfabrication techniques to create an accordion-like honeycomb microstructure in poly(glycerol sebacate), which yields porous, elastomeric three-dimensional (3D) scaffolds with controllable stiffness and anisotropy. Accordion-like honeycomb scaffolds with cultured neonatal rat heart cells demonstrated utility through: (1) closely matched mechanical properties compared to native adult rat right ventricular myocardium, with stiffnesses controlled by polymer curing time; (2) heart cell contractility inducible by electric field stimulation with directionally dependent electrical excitation thresholds (p < 0.05); and (3) greater heart cell alignment (p < 0.0001) than isotropic control scaffolds. Prototype bilaminar scaffolds with 3D interconnected pore networks yielded electrically excitable grafts with multi-layered neonatal rat heart cells. Accordion-like honeycombs can thus overcome principal structural-mechanical limitations of previous scaffolds, promoting the formation of grafts with aligned heart cells and mechanical properties more closely resembling native myocardium.