They are known to exist at the centres of most galaxies, but a puzzle remains as to how they affect galaxy evolution.
The approach, published in Nature, infers a black hole's mass from the speed of molecules swirling around it.
It could help weigh hundreds of nearby black holes. Its first use suggests a black hole in the NGC4526 galaxy has a mass 450 million times that of our Sun.
Only in a few dozen cases have the masses of supermassive black holes been estimated. Because they cannot be seen directly, astronomers have relied on guessing how large they are based on the motion of objects circling them.
Most estimates have come from gathering up starlight. This can be done by calculating how much faster the stars nearer the black hole are moving relative to those farther away.
However, that is an average measure, and the "random motions" of stars - not necessarily in the same direction as the swirling mass - blurs the measurement.
The movement of electrically charged gas can be tracked in the same way, with slightly less blurring due to random motion.