We present deep total intensity and polarization observations of the Coma cluster at 1.4 and 6.6 GHz performed with the Sardinia Radio Telescope. By combining the single-dish 1.4 GHz data with archival Very Large Array observations, we obtain new images of the central radio halo and of the peripheral radio relic where we properly recover the brightness from the large-scale structures. At 6.6 GHz, we detect both the relic and the central part of the halo in total intensity and polarization. These are the highest frequency images available to date for these radio sources in this galaxy cluster. In the halo, we find a localized spot of polarized signal, with fractional polarization of about 45 per cent. The polarized emission possibly extends along the north-east side of the diffuse emission. The relic is highly polarized, up to 55 per cent, as usually found for these sources. We confirm the halo spectrum is curved, in agreement with previous single-dish results. The spectral index is α = 1.48 ± 0.07 at a reference frequency of 1 GHz and varies from α ≃ 1.1, at 0.1 GHz, up to α ≃ 1.8, at 10 GHz. We compare the Coma radio halo surface brightness profile at 1.4 GHz (central brightness and e-folding radius) with the same properties of the other haloes, and we find that it has one of the lowest emissivities observed so far. Reanalysing the relic's spectrum in the light of the new data, we obtain a refined radio Mach number of M = 2.9 ± 0.1.