We have studied the electrodynamic response of strongly disordered superconducting TiN films using microwave resonators, where the disordered superconductor is the resonating element in a high- quality superconducting environment of NbTiN. We describe the response assuming an effective pair-breaking mechanism modifying the density of states, and compare this to local tunnelling spectra obtained using scanning tunnelling spectroscopy. For the least disordered film (kFl = 8.7, Rs = 13 {Omega}), we find good agreement, whereas for the most disordered film (kFl = 0.82, Rs = 4.3 k{Omega}), there is a strong discrepancy, which signals the breakdown of a model based on uniform properties.