Biomimetic on-chip tissue models serve as a powerful tool for studying human physiology and developing therapeutics; however, their modeling power is hindered by our inability to develop highly ordered functional structures in small length scales. Here, we demonstrate how high-precision fabrication can enable scaled-down modeling of organ-level cardiac mechanical function. We use two-photon direct laser writing (TPDLW) to fabricate a nanoscale-resolution metamaterial scaffold with fine-tuned mechanical properties to support the formation and cyclic contraction of a miniaturized, induced pluripotent stem cell-derived ventricular chamber. Furthermore, we fabricate microfluidic valves with extreme sensitivity to rectify the flow generated by the ventricular chamber. The integrated microfluidic system recapitulates the ventricular fluidic function and exhibits a complete pressure-volume loop with isovolumetric phases. Together, our results demonstrate a previously unexplored application of high-precision fabrication that can be generalized to expand the accessible spectrum of organ-on-a-chip models toward structurally and biomechanically sophisticated tissue systems.