A hand operated benchtop stamping press was developed to conduct research on microscale hole fabrication in polymer membranes for applications as scaffolds in tissue engineering. A biocompatible and biodegradable polymer, poly(ε-caprolactone), was selected for micropunching. Membranes between 30 μm and 50 μm thick were fabricated by hot melt extrusion, but could not be stamped with a 200 μm circular punch at room temperature, regardless of die clearance due to excessive strain to fracture. This problem was overcome by cooling the membrane and die sets with liquid nitrogen to take advantage of induced brittle behavior below the polymer’s glass transition temperature. While cooled, 203 μm hole patterns were successfully punched in 33 μm thick poly(ε-caprolactone) membranes with 11% die clearance, achieving 71% porosity.