The magnetically ordered states of the $A$-site ordered perovskite manganites LaBaMn${}_2$O${}_6$ and YBaMn${}_2$O${}_6$ have been investigated by muon spin relaxation in zero external magnetic field. Our data reveal striking differences in the nature of the magnetically ordered state between these materials. For LaBaMn${}_2$O${}_6$, the $\mu$SR time spectra in the ferromagnetic state below $\simeq$330 K reveal a strongly inhomogeneous phase, reminiscent of a Griffiths phase. Within this magnetically inhomogeneous phase, an antiferromagnetic state develops below 150 K, which displays well defined static internal magnetic fields, but reaches only 30$\%$ of the volume fraction at low temperatures. A broad distribution of $\mu$SR relaxation rates is inferred down to the lowest temperatures. This behavior is similar to that in the $A$-site disordered La${}_{0.5}$Ba${}_{0.5}$MnO${}_3$. On the other hand, for YBaMn${}_2$O${}_6$, the $\mu$SR time spectra for both (i) the charge and orbital ordered and (ii) the paramagnetic phases reveal rather homogeneous states, namely, an exponential relaxation in the paramagnetic state and well defined muon spin oscillation in the antiferromagnetic state.