Insulated electrically conductive fibers or microwires of sizes on the order of 1 mil (25 microns) diameter, so as to be suitable for processing into yarns or multi-microwire bundles, for example, for incorporation into conformable fabric products or for use as wearable electronic circuitry are made by coprocessing a core of a lower-melting-point metal within a sheath of a higher-melting-point polymer.