A process for manufacturing superconducting magnetic coils from strain-tolerant, superconducting multi-filament composite conductors (20) is described. The method involves winding the precursor to a multi-filament composite conductor (20) and an insulating material or its precursor around a mandrel (30) in order to form a coil (40), and then exposing the coil (40) to high temperatures and an oxidizing environment. The insulating material or its precursor is chosen to permit exposure of the superconductor precursor filaments to the oxidizing environment, and to encase the matrix-forming material (14) enclosing the filaments, which is reversibly weakened during processing.