Final answer:
No black holes have been observed emitting Hawking radiation; we detect black holes like stellar-mass and supermassive types through their gravitational effects, not Hawking radiation.
Step-by-step explanation:
No black holes have been directly observed emitting Hawking radiation yet, as this phenomenon is extremely weak and thus very difficult to detect with our current technology. To date, the best evidence of stellar-mass black holes and supermassive black holes comes from the gravitational effects they have on their surroundings, rather than from direct observation of Hawking radiation.
Stellar-mass black holes are often identified in binary systems by the motion of a visible star and X-ray emissions from the accretion disk. As for supermassive black holes, they have been discovered in the centers of galaxies, including our own Milky Way, and they power quasars and other energetic galactic nuclei.
Hawking radiation has not been observed because the radiation is expected to be weakest for more massive black holes, and our current instruments are not sensitive enough to detect such feeble emissions.