The performance of many macroscopic structures (those whose dimensions are on the order of centimeters, meters, or even larger) can be greatly improved by covering their surfaces with microstructures. There are several applications in which "large," microstructure-covered sheets are useful. An apparatus and method are disclosed for forming high aspect ratio microstructures ("HARMs") on planar and non-planar surfaces, using a modification of the LIGA microfabrication process. A free-standing polymer sheet is lithographically patterned with through-holes. The polymer sheet is then pressed against, clamped to, or otherwise attached to a conductive substrate in such a way that the patterned holes in the sheet are not blocked. Subsequent electroplating produces well-defined HARM structures on the planar or non-planar surface, in shapes that are complementary to the lithographically patterned through-holes in the polymer. The polymer may then be removed (e.g., by melting, dissolution, or burning). Various planar and non-planar surfaces have been covered with microstructures. Where the metal surface is non-planar, the polymer sheet may be heated or otherwise made sufficiently flexible to conform to the metal surface, preferably by heat-shrinking to assure firm contact. The process may be used to electroplate microstructures directly onto metal surfaces generally-not just onto metal surfaces that have been specially prepared for LIGA processes, as has previously been the case.