Rare meson decay experiments promise to measure branching ratios as small as 10(-13). This presents an opportunity to discover the mu(+)mu(-) bound state true muonium. We consider a set of possible channels, all with branching ratios above similar to 10(-11). For the electromagnetic decays eta/eta' -> (mu(+)mu(-))gamma, theoretical and phenomenological form factors F-eta/eta'gamma gamma* (Q(2)) allow predictions of BR(eta' -> (mu(+)mu(-))gamma) similar to 4.8 x 10(-10) and BR(eta' -> (mu(+)mu(-))gamma) similar to 3.7 x 10(-11) at the 5% level. Discussion of experimental prospects and potential backgrounds are made.