Microchannel scaffolds accelerate nerve repair by guiding growing neuronal processes across injury sites. Although geometry, materials chemistry, stiffness, and porosity have been shown to influence nerve growth within nerve guidance scaffolds, independent tuning of these properties in a high-throughput manner remains a challenge. Here, fiber drawing is combined with salt leaching to produce microchannels with tunable cross sections and porosity. This technique is applicable to an array of biochemically inert polymers, and it delivers hundreds of meters of porous microchannel fibers. Employing these fibers as filaments during 3D printing enables the production of microchannel scaffolds with geometries matching those of biological nerves, including branched topographies. Applied to sensory neurons, fiber-based porous microchannels enhance growth as compared to non-porous channels with matching materials and geometries. The combinatorial scaffold fabrication approach may advance the studies of neural regeneration and accelerate the development of nerve repair devices.