We studied giant magneto‐impedance (GMI) effect, magnetic and structural properties of thin Finemet‐type (FeCuNbSiB) glass‐coated microwires fabricated by Taylor‐Ulitovsky technique with different composition and diameters, with the aim to achieve the optimal conditions for improving the final GMI response. We observed that GMI can be tailored either by controlling the microwires microstructure through the thermal annealing, or by controlling the quenching rate velocity during the fabrication processes. Finally, we obtained up to 50% GMI in the as‐prepared samples and up to 100% in annealed microwires. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)