The controlled deposition of electrospun nanofibers at the micro-scale is studied. Several collectors with microscopic patterns are prepared using photolithography. Nanofiber deposition is influenced by the geometry, the size, and the distance between micro-patterns. Within certain conditions, membranes with multiple micro spider-webs or perpendicularly interconnected microgrids are obtained. Dielectric micro-holes having a conductive bottom can be filled by the nanofiber. This kind of micro-molding is rationalized using simulations that show the influence of the collector relative permittivity on the electric field at the pattern vicinity. Micro-woven membranes of PCL with good mechanical properties can be produced, allowing their use for biomedical applications in tissue engineering.