We present a method to create robust, nanoscale solid-state membranes using the natural shape of a liquid meniscus as a template. A narrow, open channel is etched into a silicon substrate and then a photoresist polymer is introduced into the channel through spontaneous capillary action. The natural concave meniscus formed by the polymer is then covered by a thin chemical vapor deposited membrane. The polymer is removed by sacrificial etching, leaving behind a suspended membrane. Membranes as large as 20 μm by 9 mm can be fabricated with a thickness as low as 50 nm.