Coulomb breakup reactions of 93,94Zr have been studied in inverse kinematics at incident beam energies of about 200 MeV/nucleon in order to evaluate neutron capture reaction methods. The 93Zr(n,γ)94Zr reaction is particularly important as a candidate nuclear transmutation reaction for the long-lived fission product 93Zr in nuclear power plants. One- and two-neutron removal cross sections on Pb and C targets were measured to deduce the inclusive Coulomb breakup cross sections, 375 ± 29 (stat.) ± 30 (syst.) and 403 ± 26 (stat.) ± 31 (syst.) mb for 93Zr and 94Zr, respectively. The results are compared with estimates using the standard Lorentzian model and microscopic calculations. The results reveal a possible contribution of the pygmy dipole resonance or giant quadrupole resonance in the Coulomb breakup reactions of 94Zr.