We fabricate contacts to molecular circuits by evaporating metal through a nanoscale stencil mask etched in a free-standing silicon nitride membrane. In this way, contacts can be fabricated on as-grown molecular wires that would be contaminated or destroyed by chemicals and heat treatments associated with conventional lithographic techniques. Chemical vapor deposition-grown single-walled carbon nanotubes contacted in this fashion behave similarly to samples contacted using conventional lithography but are more robust to failure at high bias. In-vacuum electrical measurements of λ-DNA networks on mica substrates contacted in a “leads-on-top” geometry give a lower bound of 1000 TΩ for the resistance of a 1-μm length of DNA.