We compare the results of a large grid of N-body simulations with the surface brightness and velocity dispersion profiles of the globular clusters {omega} Cen and NGC 6624. Our models include clusters with varying stellar-mass black hole retention fractions and varying masses of a central intermediate-mass black hole (IMBH). We find that an ~45000M_{sun}_ IMBH, whose presence has been suggested based on the measured velocity dispersion profile of {omega} Cen, predicts the existence of about 20 fast-moving, m>0.5M_{sun}_, main-sequence stars with a (1D) velocity v>60km/s in the central 20arcsec of {omega} Cen. However, no such star is present in the HST/ACS proper motion catalogue of Bellini et al. (2017ApJ...842....6B, Cat. J/ApJ/842/6), strongly ruling out the presence of a massive IMBH in the core of {omega} Cen. Instead, we find that all available data can be fitted by a model that contains 4.6 per cent of the mass of {omega} Cen in a centrally concentrated cluster of stellar-mass black holes. We show that this mass fraction in stellar-mass BHs is compatible with the predictions of stellar evolution models of massive stars. We also compare our grid of N-body simulations with NGC 6624, a cluster recently claimed to harbour a 20000M_{sun}_ black hole based on timing observations of millisecond pulsars. However, we find that models with M_IMBH_>1000M_{sun}_ IMBHs are incompatible with the observed velocity dispersion and surface brightness profile of NGC 6624, ruling out the presence of a massive IMBH in this cluster. Models without an IMBH provide again an excellent fit to NGC 6624.