In a model-independent way, we explore the potential of photon-induced interactions with the process gamma*gamma* -> ZZ to investigate CP-conserving and CP-violating dimension-six operators of Higgs-gauge boson couplings using the standard model effective field theory. The existence of anomalous H gamma gamma and HZZ couplings is discussed at 3 TeV compact linear collider (CLIC) and 10 TeV muon collider (MuC) with integrated luminosities of 5 and 10 ab-1, respectively. All signal and relevant background events are generated in MadGraph and passed through PYTHIA for parton showering and hadronization. The detector effects are evaluated using CLIC and MuC detector cards tuned in Delphes. We report the 95% confidence level limits on the Wilson coefficients c <overline> gamma , c <overline> HB , c <overline> HW , c gamma , c HB , and c HW and compare them with the experimental and phenomenological limits.