This paper describes soft lithography methods that expand current fabrication capabilities by enabling high-throughput patterning on nonplanar substrates These techniques exploit optically dense elastomeric mask elements embedded in a transparent poly(dimethylsiloxane) (PDMS) matrix by vacuum-assisted microfluidic patterning, UV-ozone-mediated irreversible sealing, and chemical etching. These protocols provide highly flexible photomasks exhibiting either positive- or negative-image contrasts, which serve as amplitude masks for large-area photolithographic patterning on a variety of curved (and planar) surfaces. When patterning on cylindrical surfaces, the developed masks do not experience significant pattern distortions. For substrates with 3D curvatures/geometries, however, the PDMS mask must undergo relatively large strains in order to make conformal contact. The new methods described in this report provide planar masks that can be patterned to compliantly compensate for both the displacements and distortions of features that result from stretching the mask to span the 3D geometry. To demonstrate this, a distortion-corrected grid pattern mask was fabricated and used in conjunction with a homemade inflation device to pattern an electrode mesh on a glass hemisphere with predictable registration and distortion compensation The showcased mask fabrication processes are compatible with a broad range of substrates, illustrating the potential for development of complex lithographic patterns for a variety of applications in the realm of curved electronics (i.e., synthetic retinal implants and curved LED arrays) and wide field-of-view optics.