We obtain predictions for a number of radiative decays \(B_{(s)}\to V\gamma\), \(V\) the vector meson, which proceed through the weak-annihilation mechanism. Within the factorization approximation, we take into account the photon emission from the \(B\)-meson loop and from the vector-meson loop; the latter subprocesses were not considered in the previous analyses but are found to have sizeable impact on the \(B_{(s)}\to V\gamma\) decay rate. The highest branching ratios for the weak-annihilation reactions reported here are \({\cal B}(\bar B^0_s\to J/\psi\gamma)=1.5\cdot 10^{-7}\) and \({\cal B}(B^-\to \bar D_s^{*-}\gamma)=1.7\cdot 10^{-7}\), the estimated accuracy of these predictions being at the level of 20\%.