Sr2MgWO6 (SMW) is a typical perovskite oxide compound, but there has been little research on the effects of processing on its dielectric properties. In this work, SMW ceramics were prepared by solid-state synthesis with sintering at 1450 °C, 1475 °C, 1500 °C and 1525 °C, respectively. XRD results confirmed that the samples possessed double perovskite structure (Fm-3m). The Raman and FTIR spectra were used to study the lattice vibrational modes. The FPSQ model was used to obtain the fitting curves of the FTIR spectra and derive the intrinsic properties of the material that were found to be in agreement with the measured data. The structure-property relationships were successfully established based on the Raman mode results. The optimal sintering temperature of SMW ceramics was identified as 1475 °C due to the excellent performances characteristics (εr = 16.97, Q × f = 23,872 GHz, τf = −35.38 ppm/°C) obtained at this temperature. This study explored the relationships among the crystal structures, lattice vibrational characteristics and dielectric properties of SMW ceramics, so as to further understand their dielectric response mechanism and lay a solid theoretical foundation for the development of microwave ceramics.