We consider the production of J/psi and psi (2S) mesons originating from the decays of b-flavored hadrons at the LHC using the k_T-factorization approach. Our analysis covers both inclusive charmonia production and production of J/psi mesons in association with Z bosons. We apply the transverse momentum dependent (or unintegrated) gluon density in a proton derived from Catani–Ciafaloni–Fiorani–Marchesini (CCFM) evolution equation and adopt fragmentation functions based on the non-relativistic QCD factorization to describe the inclusive b-hadron decays into the different charmonium states. Our predictions agree well with latest experimental data taken by the CMS, ATLAS and LHCb Collaborations at sqrt{s} = 7, 8 and 13 TeV. The contributions from double parton scattering to the associated non-prompt J/psi + Z production are estimated and found to be small.