We study black-hole ringdown in the presence of exceptional points (EPs) using a hyperboloidal framework that extends the standard quasinormal-mode (QNM) description. Near EPs, we find the near-coalescence of both QNM eigenvalues and eigenfunctions, giving rise to genuine resonant behavior that is not captured by conventional QNM analyses. Using a phenomenological environmental black-hole model evolved on hyperboloidal slices, we show that these spectral features lead to enhanced mode contributions and characteristic departures from simple exponentially damped oscillations in the time domain. We further identify the EP frequency, given by the averaged value of the interacting modes, as the physically relevant observable in the near-EP regime.