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Abstract A search for the very rare$$B^{*0}\rightarrow \mu ^+\mu ^-$$ $B_{}^{\ast 0}\to {\mu }^{+}{\mu }^{-}$and$$B_{s}^{*0}\rightarrow \mu ^+\mu ^-$$ $B_s^{\ast 0}\to {\mu }^{+}{\mu }^{-}$decays is conducted by analysing the$$B_c^+\rightarrow \pi ^+\mu ^+\mu ^-$$ $B_c^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$process. The analysis uses proton-proton collision data collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9$$\text {\,fb}^{-1}$$ ${\text{,fb}}^{-1}$. The signal signatures correspond to simultaneous peaks in the$$\mu ^+\mu ^-$$ ${\mu }^{+}{\mu }^{-}$and$$\pi ^+\mu ^+\mu ^-$$ ${\pi }^{+}{\mu }^{+}{\mu }^{-}$invariant masses. No evidence for an excess of events over background is observed for either signal decay mode. Upper limits at the$$90\%$$ $90\%$confidence level are set on the branching fractions relative to that for$$B_c^+\rightarrow J\hspace{-1.66656pt}/\hspace{-1.111pt}\psi \pi ^+$$ $B_c^{+}\to J/\psi {\pi }^{+}$decays,$$\begin{aligned} \mathcal{R}_{B^{*0}(\mu ^+\mu ^-)\pi ^+/J\hspace{-1.66656pt}/\hspace{-1.111pt}\psi \pi ^+}&< 3.8\times 10^{-5}\ \text { and }\\ \mathcal{R}_{B_{s}^{*0}(\mu ^+\mu ^-)\pi ^+/J\hspace{-1.66656pt}/\hspace{-1.111pt}\psi \pi ^+}&< 5.0\times 10^{-5}. \end{aligned}$$ $\begin{array}{cc}R_{B_{}^{\ast 0}\left({\mu }^{+}{\mu }^{-}\right){\pi }^{+}/J/\psi {\pi }^{+}}^{}& <3.8\times {10}^{-5}\text{and}\\ R_{B_s^{\ast 0}\left({\mu }^{+}{\mu }^{-}\right){\pi }^{+}/J/\psi {\pi }^{+}}^{}& <5.0\times {10}^{-5}.\end{array}$