Is there any experimental evidence for Hawking radiation? "Physical insight into the process may be gained by imagining that particle–antiparticle radiation is emitted from just beyond the event horizon. This radiation does not come directly from the black hole itself, but rather is a result of virtual particles being "boosted" by the black hole's gravitation into becoming real particles. As the particle–antiparticle pair was produced by the black hole's gravitational energy, the escape of one of the particles lowers the mass of the black hole."
How can virtual particle become real particles? It involves an energy transfer from the potential energy of the black to the virtual particles?
"An alternative view of the process is that vacuum fluctuations cause a particle–antiparticle pair to appear close to the event horizon of a black hole. One of the pair falls into the black hole while the other escapes. In order to preserve total energy, the particle that fell into the black hole must have had a negative energy (with respect to an observer far away from the black hole). This causes the black hole to lose mass, and, to an outside observer, it would appear that the black hole has just emitted a particle."
What does it mean for a particle to have a negative energy wrt an observer outside the black hole?
"In another model, the process is a quantum tunnelling effect, whereby particle–antiparticle pairs will form from the vacuum, and one will tunnel outside the event horizon."
Can this prediction be tested experimentally? Is there any progress in this direction so far?
 A: There are several physical systems that can be analogous to a black hole. One of which is the sonic/acoustic black hole (or dumb hole) in which phonons can't escape a Bose-Einstein condensate that flows faster than local speed of sound, in a similiar manner to photons that can't escape the gravity well of a black hole.
In such an apparatus, Beckenstein-Hawking radiation analogue was measured expiramentally, for example:
Steinhauer, J. (2014). Observation of self-amplifying Hawking radiation in an analogue black-hole laser. Nature Physics, 10(11), 864-869. doi:10.1038/nphys3104
A: Although I don't see anything wrong with the 2017 answer by "A. Ok" (which answered the OP's secondary question about progress being made in experimental verification of Hawking radiation's existence), I realize that it does not completely answer the OP's title question, primarily because of possible differences between sound (whose energetic effects result from interactions between fermions comprising at least part of a massive medium, usually air) and light (which consists entirely of bosons, that differ from fermions in such important respects as their ability to pass through each other).  These differences may account for conclusions "within 6 percent" of those hypothesized for the experiment, which seems rather low by scientific standards.
Consequently, I'd like to point out an analysis of observational data that has been rather authoritatively considered to answer the OP's title question:  Found in the Mar.2, 2020, preprint of a paper titled "Apparent Evidence for Hawking points in the CMB Sky", by Daniel An, Krzysztof A. Meissner, Pawel Nurowski, and Roger Penrose. it interprets "several anomalous spots of significantly raised temperature" in the Cosmic Microwave Background as Hawking radiation, and appears to have been the decisive factor in the award (on October 6, 2020) of a Nobel Prize, in Physics, to the mathematical physicist Sir Roger Penrose.
The Nobel Prize Committee's report can be found at https://www.nobelprize.org/uploads/2020/10/advanced-physicsprize2020.pdf , or by cutting & pasting its title ("Theoretical Foundation for Black Holes and the Supermassive Compact Object at the Galactic Centre") into any search box.  The report includes a short bibliography of some of the related works by Penrose and others.
Regarding the OP's secondary question about energy, virtual particles are made real by the gravitational field of the black hole, as described by Gasperini, Veneziano, and others, with Gasperini's description of the process (as resulting from separation of the members of a virtual particle/antiparticle pair by more than the Compton wavelength during more than the Compton time) available through public libraries (either directly or via inter-library loan) in "Gasperini, M. 1986, PhRvL, 56, 2873".  (Although "popular science" texts, such as Appendix A in the 1997 version of Guth's book titled "The Inflationary Universe", often refer to it as "negative energy", and although even Einstein was not particularly fond of the alternative geometrical interpretation that refers to it as the curvature of spacetime, gravity is not consistently considered to be strictly "energy" in the terminology of physics:  However, because of gravity's extreme and possibly infinite range, as well as its extreme weakness [with practically any toy magnet able to overcome its strength by lifting a needle from a table top], no boson comprising it is likely to be discovered any time soon.)
