One of the greatest challenges currently faced in tissue engineering is the incorporation of vascular networks within tissue-engineered constructs. The aim of this study was to develop a technique for producing a perfusable, 3-dimensional, cell-friendly model of vascular structures that could be used to study the factors affecting angiogenesis and vascular biology in engineered systems in more detail. Initially, biodegradable synthetic pseudovascular networks were produced via the combination of robocasting and electrospinning techniques. The internal surfaces of the vascular channels were then recellularized with human dermal microvascular endothelial cells (HDMECs) with and without the presence of human dermal fibroblasts (HDFs) on the outer surface of the scaffold. After 7 days in culture, channels that had been reseeded with HDMECs alone demonstrated irregular cell coverage. However, when using a co-culture of HDMECs inside and HDFs outside the vascular channels, coverage was found to be continuous throughout the internal channel. Using this cell combination, collagen gels loaded with vascular endothelial growth factor were deposited onto the outer surface of the scaffold and cultured for a further 7 days. After this, endothelial cell outgrowth from within the channels into the collagen gel was observed, showing that the engineered vasculature maintains its capacity for angiogenesis. Furthermore, the HDMECs appeared to have formed perfusable tubules within the gel. These results show promising steps towards the development of an in vitro platform for studying angiogenesis and vascular biology in a tissue engineering context.