We investigate the microwave properties of epoxy-based composite containing melt-extracted CoFeBSiNb microwires fabricated by a combined current-modulation annealing (CCMA) technique. We observe a shift of the resonance peak in the effective permittivity spectra of the composite sample containing annealed 25 mm Nb-doped microwires as an applied magnetic field is increased. This observation is consistent with the absorption-dominated impedance for thick microwires and the ferromagnetic resonance phenomenon. It is shown that CCMA is an appropriate technique to release internal residual stresses. Hence, for samples containing small amounts of Nb, we observe that CCMA allows us to suppress the high frequency resonance peak observed in samples containing as-cast wires. However, for samples containing a high amount of Nb, the high frequency peak remains despite the CCMA treatment. In this case, the observation of a two-peak feature in the permittivity spectra is attributed to the coexistence of the amorphous phase and a small amount of nanocrystallites distributed at the wire surface. However, due to large magnetostatic energy of long (35 mm) and short (15 mm) as-cast wires and imperfect wire-epoxy bonding no shift of the resonance peak and the characteristic double peak of the permittivity spectrum can be detected. Overall, CCMA emerges as a promising strategy to control microwave permittivity in composites with melt-extracted microwires.