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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 $\sim 45,000$ M$_\odot$ IMBH, whose presence has been suggested based on the measured velocity dispersion profile of $\omega$ Cen, predicts the existence of about 20 fast-moving, $m>0.5$ M$_\odot$ main-sequence stars with a (1D) velocity $v>60$ km/sec in the central 20 arcsec of $\omega$ Cen. However no such star is present in the HST/ACS proper motion catalogue of Bellini et al. (2017), 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% 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 harbor a 20,000 M$_\odot$ black hole based on timing observations of millisecond pulsars. However, we find that models with $M_{IMBH}>1,000$ M$_\odot$ 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.