  The tools of Kerr/CFT correspondence are applied to the Kerr black hole
embedded in an axial external magnetic field. Its extremal near horizon
geometry remains a warped and twisted product of $AdS_2\times S^2$. The central
charge of the Virasoro algebra, generating the asymptotic symmetries of the
near horizon geometry, is found. It is used to reproduce, via the Cardy
formula, the Bekenstein-Hawking entropy of the magnetised Kerr black hole as
the statistical microscopic entropy of a dual CFT. The presence of the
background magnetic field makes available also a second dual CFT picture, based
on the $U(1)$ electromagnetic symmetry, instead of the only rotational one of
the standard non-magnetised Kerr spacetime. A Meissner-like effect, where at
extremality the external magnetic field is expelled out of the black hole,
allows us to infer the value of the mass for these magnetised extremal black
holes. The generalisation to the CFT dual for the magnetised extreme
Kerr-Newman black hole is also presented.
