By definition, nothing radiates from a black hole. In order to detect it, we'll have to use indirect methods.
If the black hole belongs to a binary system, we can think of two methods :
The diameter of the object is at least equal to the speed of light multiplied by the time interval between two extremes of brightness.
If the black hole is alone, these methods are, of course, no use. A lone black hole has been detected by a gravitational micro-lensing effect : its highly concentrated mass diverted the light of stars behind it.
Source : NASA - Notre Dame University (Indiana)
Do black hole actually exist, or are they only neutron stars ?
In order to be sure, examining such an object in a binary system
may be a solution, especially its accretion
Closer to the central star, the gravity is higher, and so the redshift of the X-ray emission is more important, due to the hot circulating gas.
The disk appears redder and weaker near the central star.
If this star is a black hole, when the gas goes behind the horizon, it completely disappears, and the emission vanishes.
Besides the redshift of the radiated light, due to the intense gravitational
field of the central star, you can observe the complete fading of light
emission near the center, in the case of a black hole.
On the opposite side, a neutron star has a solid surface, and there is a peak in the brightness, where the gas collides with it.
The Chandra satellite is a telescope which is sensitive to the X-ray part of the spectrum. Thanks to this satellite, one can observe the nova phenomenon in binary systems with an ultra-compact star.
X-ray radiation from some of these novae appears to be 100 to 1000 times weaker than others. This fact seems to demonstate the reality of black holes, following the above arguments.