  In a model-independent way, we explore the potential of photon-induced
interactions with the process $\gamma^* \gamma^* \rightarrow ZZ$ to investigate
CP-conserving and CP-violating dimension-six operators of Higgs-gauge boson
couplings using the Standard Model Effective Field Theory (SMEFT). 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 $\overline{c}_\gamma$,
$\overline{c}_{HB}$, $\overline{c}_{HW}$, $\widetilde{c}_\gamma$,
$\widetilde{c}_{HB}$, and $\widetilde{c}_{HW}$ and compare them with the
experimental and phenomenological limits.
