We show tuning of the resonance frequency of aluminum nanoantennas via variation of the refractive index n of a layer of phase-change material. Three configurations have been considered, namely, with the antennas on top of, inside, and below the layer. Phase-change materials offer a huge index change upon the structural transition from the amorphous to the crystalline state, both stable at room temperature. Since the imaginary part of their permittivity is negligibly small in the mid-infrared spectral range, resonance damping is avoided. We present resonance shifting to lower as well as to higher wavenumbers with a maximum shift of 19.3% and a tuning figure of merit, defined as the resonance shift divided by the full-width at half-maximum (FWHM) of the resonance peak, of 1.03.