Low-K microwave dielectric ceramics are pivotal in 5G and millimetre-wave communications. Among them, garnet-structured ceramics hold significant strategic importance because of their rich elemental composition and high Q × f values. In this study, we investigated garnet-structured Ca₃Mn₂Ge₃O₁₂, aiming to optimize the ceramic phase composition through the synthesis of Ca₃Mn_2+xGe₃O_12+δ (x = 0–0.2) ceramics. XRD analysis revealed a pure phase of Ca₃Mn₂Ge₃O₁₂ (PDF#00-034-0285) only when x = 0.1, whereas impurity phases were observed for all other components. Rietveld refinement confirmed the garnet structure of the samples with the Iad space group. The highest bulk (4.383 g cm⁻³) and relative (96.34%) densities were achieved after sintering at 1190 °C, when the radial shrinkage reached 11.5%. At a sintering temperature of 1180 °C, the ceramics displayed excellent microwave dielectric properties: ε_r = 8.88, Q × f = 50 793 GHz, τ_f = −39.35 ppm °C⁻¹. Raman, XPS, and Rietveld refinement data respectively revealed that the relative density of the ceramics was closely related to the dielectric constant; the relative Mn³⁺/Mn⁴⁺ content, packing fraction, and FWHM of the A_1g Raman spectra were highly correlated with the Q × f value; and the Mn–O bond valence affected the Q × f and τ_f values of the samples. Furthermore, far-infrared reflectance spectroscopy indicated a theoretical Q × f value of ∼130 000 GHz, suggesting that the existing samples have potential for further development. In conclusion, Ca₃Mn_2+xGe₃O_12+δ (x = 0.1) ceramics with optimised phase compositions have great potential for development and application in 5G and millimetre-wave communications.