We present a theoretical study of the formation of self-trapped excitons (STEs) and the associated broadband emission in metal-halide perovskites Cs4SnBr6 and Cs2AgInCl6, using time-dependent density functional theory (TDDFT) with the dielectric-dependent hybrid (DDH) functional. Our approach allows for an accurate description of the excitonic effect and geometry relaxation in the electronic excited states and yields optical gap, STE emission energy, and emission spectra in reasonable agreement with experiments. We point out the significance of considering geometry relaxations in the electronic excited state by showing that the exciton-phonon coupling computed in the ground-state atomic geometry is insufficient to describe the physical properties of STEs. Overall, we find that TDDFT with the DDH hybrid functional is a suitable approach for the study of the formation of STEs in perovskite and provides insights for designing metal-halide perovskites with tailored emission properties.