A search for decays of the Higgs and Z boson to pairs of $\mathrm{J}/\psi$ or $\Upsilon(\text{nS})$ (n=1,2,3) mesons, with their subsequent decay to $\mu^{+}\mu^{-}$ pairs, is presented. The analysis uses data from proton-proton collisions at $\sqrt{s} =$ 13 TeV, collected with the CMS detector at the LHC in 2017 and corresponding to an integrated luminosity of 37.5 fb$^{-1}$. While an observation of such a decay with this sample would indicate the presence of physics beyond the standard model, no significant excess is observed. Upper limits at 95% confidence level are placed on the branching fractions of these decays. In the $\mathrm{J}/\psi$ pair channel, the limits are $1.8 \times 10^{-3}$ and $2.2 \times 10^{-6}$ for the Higgs and Z boson, respectively, while in the combined $\Upsilon(\text{nS})$ pair channel, the limits are $1.4 \times 10^{-3}$ and $1.5 \times 10^{-6}$, respectively, when the mesons from the Higgs and Z boson decay are assumed to be unpolarized. When fully longitudinal and transverse polarizations are considered the limits reduce by about 22-29% and increase by about 10-13%, respectively.

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