Ceramic Ba_0.6Sr_0.4TiO₃ (BST-0.6) samples were studied in the broad spectral range of 10⁶–10¹⁴ Hz by using several dielectric techniques in between 20 and 800 K. The dominant dielectric dispersion mechanism in the paraelectric phase was shown to be of strongly anharmonic soft-phonon origin. The whole soft-mode response in the vicinity of the ferroelectric transition was shown to consist of two coupled overdamped THz excitations, which show classical features of a coupled soft and central mode, known from many ferroelectric crystals with a dynamics near the displacive and order–disorder crossover. Similar behaviour has been recently revealed and theoretically simulated in pure BaTiO₃ (see Ponomareva et al 2008 Phys. Rev. B 77 012102 and Hlinka et al 2008 Phys. Rev. Lett. 101 167402). Also for the BST system, this feature was confirmed by the theory based on molecular dynamics simulations with an effective first-principles Hamiltonian. In all the ferroelectric phases, additional relaxation dispersion appeared in the GHz range, assigned to ferroelectric domain-wall dynamics. The microwave losses were analysed from the point of view of applications. The paraelectric losses above 1 GHz are comparable with those in single crystals and appear to be of intrinsic multi-phonon origin. The ceramic BST system is therefore well suited for applications in the whole microwave range.