Magnetic and magnetotransport properties of glass-covered amorphous microwires of nominal composition Fe₈₉B₁Si₃C₃Mn₄ have been studied. Samples of two families with the same composition but different metallic core diameters were annealed in a furnace or by Joule heating. The electrical resistance was measured as a function of time during annealing to study the effects on the samples' microstructures (evolution from the amorphous to the crystalline phase). Static hysteresis loops were measured on all samples by means of a vibrating sample magnetometer. Giant magneto-impedance measurements (GMI) performed on a coaxial line using a vectorial network analyser at frequencies up to 6 GHz showed that furnace-annealed samples display larger anisotropies with respect to Joule-heated ones; however, Joule heating is more effective in improving the magneto-impedance response of the alloy. The maximum GMI ratio is ≈ 175% at 4 GHz. The influence of the different metallic core/total wire diameter on the induced anisotropies has been studied for the two families of samples through hysteresis loops and high-frequency GMI.