We investigate a possibility to find an accreting isolated black hole (IBH) with mass 1—100 M_☉ within Central Galactic Molecular Zone in the submillimetre and infrared spectral range with help of planned space observatories James Webb Space Telescope (JWST) and Millimetron (MM). We assume the spherical mode of accretion. We develop the simplest possible quantitative model of the formation of radiation spectrum in this range due to synchrotron emission and show that it fully agrees with the more complicated model of Ipser and Price (1982) for expected values of accretion rate. If a substantial fraction of the Laser Interferometer Gravitational-Wave Observatory (LIGO) events was caused by merger of primordial black holes, the JWST would be able to find them provided that there is a cusp in distribution of dark matter in the Galaxy and that the accretion efficiency parameter λ defined as the ratio of accretion rate on to IBH to its Bondi-Hoyle-Lyttleton value is larger than ∼10^-2. A comparable amount of IBHs is also predicted by recent models of their formation due to stellar evolution. MM capabilities are hampered by the effect of confusion due to distant submillimetre galaxies, but it can also be used for such purposes if the confusion effect is properly dealt with. In case of efficient accretion with λ ∼ 1, both instruments could detect IBHs even when their number densities are as low as 10^-6 pc^-3.

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