Printing human tissue constructs replete with biomimetic vascular networks is of growing interest for tissue and organ engineering. While it is now possible to embed perfusable channels within acellular and densely cellular matrices, they lack either the branching or multilayer architecture of native vessels. Here, we report a generalizable method for printing hierarchical branching vascular networks within soft and living matrices. We embed biomimetic vessels into granular hydrogel matrices via coaxial embedded printing (co-EMB3DP) as well as into bulk cardiac tissues via coaxial sacrificial writing into functional tissues (co-SWIFT). Each method relies on an extended core-shell printhead that promote facile interconnections between printed branching vessels. Though careful optimization of multiple core-shell inks and matrices, we show that embedded biomimetic vessels can be coaxially printed, which possess a smooth muscle cell-laden shell that surrounds perfusable lumens. Upon seeding these vessels with a confluent layer of endothelial cells, they exhibit good barrier function. As a final demonstration, we construct biomimetic vascularized cardiac tissues composed of a densely cellular matrix of cardiac spheroids derived from human induced pluripotent stem cells. Importantly, these co-SWIFT cardiac tissues mature under perfusion, beat synchronously, and exhibit a cardio-effective drug response in vitro. This advance opens new avenues for the scalable biomanufacturing of organ-specific tissues for drug testing, disease modeling, and therapeutic use.