Hawking radiation of astrophysical black holes is minute and thought to be unobservable. However, different mechanisms could contribute to an anomalously high emission rate: extra dimensions, new "dark" families of bosons or fermions, or a lower fundamental Planck scale. Do black holes flood the Universe with gravitational waves via mass loss? Here, we show that the formation of black hole binaries and the absence of a stochastic background of gravitational waves can limit the emission rate to vertical bar(M) over dot vertical bar less than or similar to 10(-15) M-circle dot/yr (vertical bar(M) over dot vertical bar less than or similar to 10(-13) M-circle dot/yr), when the mass loss branching ratio to gravitons is unity (10(-2)). This constraint is up to seven orders of magnitude more stringent than hounds from resolvable inspiralling binaries.