Microvascular networks are essential for the efficient transport of nutrients, waste products, and drugs throughout the body. Wire-templating is an accessible method for generating laboratory models of these blood vessel networks, but it has difficulty fabricating microchannels with diameters of ten microns and narrower, a requirement for modeling human capillaries. This study describes a suite of surface modification techniques to selectively control the interactions amongst wires, hydrogels, and world-to-chip interfaces. This wire templating method enables the fabrication of perfusable hydrogel-based rounded cross-section capillary-scale networks whose diameters controllably narrow at bifurcations down to 6.1 ± 0.3 microns in diameter. Due to its low cost, accessibility, and compatibility with a wide range of common hydrogels of tunable stiffnesses such as collagen, this technique may increase the fidelity of experimental models of capillary networks for the study of human health and disease.