A conformally Kaehler, Einstein-Maxwell (cKEM for short) metric is a Hermitian metric with constant scalar curvature on a compact complex manifold such that it is conformal to a Kaehler metric with conformal factor being a Hamiltonian Killing potential. Fixing a Kaehler class, we characterize such Killing vector fields whose Hamiltonian function with respect to some Kaehler metric in the fixed Kaehler class gives a cKEM metric. The characterization is described in terms of critical points of certain volume functional. The conceptual idea is similar to the cases of Kaehler-Ricci solitons and Sasaki-Einstein metrics since the derivative of the volume functional gives rise to a natural obstruction to the existence of cKEM metrics. This talk is based joint works with Hajime Ono.