Black holes have the peculiar and intriguing property of having an event horizon, a one-way membrane causally separating their internal region from the rest of the Universe. Today, astrophysical observations provide some evidence for the existence of event horizons in astrophysical black hole candidates. In this short paper, I compare the constraint we can infer from the nonobservation of electromagnetic radiation from the putative surface of these objects with the bound coming from the ergoregion instability, pointing out the respective assumptions and limitations.