The magnetotunable left-handed characteristics of Fe(77.5)Si(12.5)B(10) glass-coated ferromagnetic microwires are analyzed in array and single microwire configuration, employing a rectangular waveguide working in X band. While the negative permeability is ascribed to the natural ferromagnetic resonance (NFMR) of the highly and positive magnetostrictive microwire, the negative permittivity features of the medium are attributed to the interaction of the microwires with the metallic rectangular waveguide. The dependence of the NFMR frequency on the applied external magnetic field enables the design of magnetotunable left-handed systems with wide-frequency band.