The dielectric properties of (1 − x)Ba(Zn_1/3Nb_2/3)O₃–xBa (Ga_1/2Ta_1/2)O₃ (BZN–xBGT) microwave (MW) ceramics, with x between 0 and 0.2, and those of 0.9Ba(Zn_0.6Co_0.4)_1/3Nb_2/3O₃–0.1Ba(Ga_0.5Ta_0.5)O₃ (BZCN–BGT) were studied at MW, terahertz (THz) and infrared (IR) frequencies at temperatures from 10 to 300 K. At room temperature, the temperature coefficient of resonance frequency (τ_f) near 3 GHz decreases from 28 ppm K⁻¹ in undoped BZN to 2 ppm K⁻¹ in BZN–0.2BGT and reduces to zero in BZCN–BGT. The addition of BGT to BZN depresses the dielectric Q value, but incorporation of Co improves the Q values, yielding Q ~ 30 000 at 3 GHZ in BZCN–BGT. The relative permittivity (ε') exhibits only limited variation with composition (ε' values in the range 34.4–36.0). IR and THz spectra as well as the low-temperature MW dielectric measurements revealed a weak dielectric relaxation below phonon frequencies, possibly arising from charges caused by inhomogeneous distribution of the B-site ions with differing valences. The IR reflectivity spectrum of BZN–0.2BGT is significantly different (smeared) compared with other compositions, which may be caused by disorder on the B sites and by an amorphous phase at the grain boundaries.