We propose to characterize the basic muonium/hydrogen configurations in selected rare-earth sesquioxides with the basic crystallographic structures: neodymium oxide (hexagonal A form), samarium oxide (monoclinic B form) and lutetium oxide (cubic bixbyite C form). Transverse-field measurements at 2G and 100G are intended at 10K in order to identify the presence of deep-acceptor like or shallow-donor-like configurations. Temperature dependence studies are also proposed in order to identify muonium dynamics and attempt at determining the corresponding levels. Ancillary repolarization measurements are intended to address the hyperfine and superhyperfine interactions involved.