  Standard Model $ZZ$ production is an important background for many searches
at the LHC, especially in final states with missing transverse momentum. In
this article, boson substitution is applied to estimate $ZZ \rightarrow \ell^+
\ell^- \nu \bar{\nu}$ yields from $Z\gamma \rightarrow \ell^+ \ell^- \gamma$
events. The cross-section ratio of the two processes and its uncertainties are
evaluated at NNLO with the MATRIX generator as a function of the transverse
momentum of the substituted boson. Uncertainties due to higher-order QCD
corrections, parton distribution functions, photon isolation criteria, and
electroweak corrections are evaluated. They depend strongly on the applied
event selections and the considered transverse momentum range. For minimal
selections, their size is 3$-$4%, dominated by QCD-related uncertainties for
transverse momenta below 500 GeV and by uncertainties due to the factorization
of QCD and electroweak corrections at higher transverse momenta.
