Spin and lattice dynamics of CaMn7O12 ceramics were investigated using infrared, THz and inelastic neutron scattering (INS) spectroscopies in the temperature range 2 to 590 K, and, at low temperatures, in applied magnetic fields of up to 12 T. On cooling, we observed phonon splitting accompanying the structural phase transition at Tc = 450K as well as the onset of the incommensurately modulated structure at 250 K. In the two antiferromagnetic phases below T_N1 = 90K and T_N2 = 48 K, several infrared-active excitations emerge in the meV range; their frequencies correspond to the maxima in the magnon density of states obtained by INS. At the magnetic phase transitions, these modes display strong anomalies and for some of them, a transfer of dielectric strength from the higher-frequency phonons is observed. We propose that these modes are electromagnons. Remarkably, at least two of these modes remain active also in the paramagnetic phase; for this reason, we call them paraelectromagnons. In accordance with this observation, quasielastic neutron scattering revealed short-range magnetic correlations persisting within temperatures up to 500K above T_N1.