Heart regeneration after myocardial infarction (MI) using human stem cell-derived cardiomyocytes (CMs) is rapidly accelerating with large animal and human clinical trials. However, vascularization methods to support the engraftment, survival, and development of implanted CMs in the ischemic environment of the infarcted heart remain a key and timely challenge. To this end, we developed a dual remuscularization-revascularization therapy that is evaluated in a rat model of ischemia-reperfusion MI. This study details the differentiation of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) for engineering cardiac tissue containing patterned engineered vessels 400 μm in diameter. Vascularized engineered human myocardial tissues (vEHMs) are cultured in static conditions or perfused in vitro prior to implantation and evaluated after two weeks. Immunohistochemical staining indicates improved engraftment of hiPSC-CMs in in vitro-perfused vEHMs with greater expression of SMA+ vessels and evidence of inosculation. Three-dimensional vascular reconstructions reveal less tortuous and larger intra-implant vessels, as well as an improved branching hierarchy in in vitro-perfused vEHMs relative to non-perfused controls. Exploratory RNA sequencing of explanted vEHMs supports the hypothesis that co-revascularization impacts hiPSC-CM development in vivo. Our approach provides a strong foundation to enhance vEHM integration, develop hierarchical vascular perfusion, and maximize hiPSC-CM engraftment for future regenerative therapy.