The Museum of the Serbian Orthodox Church sits in the Patriarchate building near Belgrade's cathedral, so it is easy to fold into a walk through the old core rather than treat as a separate excursion. Its collection is quiet but rich: icons, church textiles, manuscripts, metalwork, and objects tied to the long institutional memory of the Serbian Orthodox Church.
It is most rewarding if you already have some interest in Serbian history or religious art. The museum does not have the spectacle of Belgrade's larger sights, but it gives useful context for the city's churches and for the role Orthodoxy has played in Serbian identity.