Observations of the Black Widow binary containing millisecond pulsar B1957+20: the X-ray tail emission detected by Chandra (Huang et al. 2012) and the pulsed, phase averaged γ-ray emission discovered by Fermi (Guillemot et al. 2012) are compared with the calculations of the IC and the synchrotron emission by relativistic electrons in the nebula around this system. The γ-ray spectra are produced by the electrons which scatter both the MBR and the infrared photons from the galactic disk. The electrons have a power law spectrum with the index of −2.1 between E_w = 3 TeV and E_max = 160 TeV, given by Eq. (4) (thick dashed curves). The other parameters of the model are: the magnetization parameter σ = 0.01, the location of the shock R_sh = 10¹⁶ cm, the minimum magnetic field strength B_min = 0.5   μG, the confinement region of the electrons has the radius of R_Neb = 5 pc. The 100 h differential sensitivity of the MAGIC stereo system is marked by the thin dotted curve (Aleksic et al. 2012) and 100 h CTA sensitivity is marked by the thin dot-dashed curve (Actis et al. 2011).