Three kinds of ceramics, zirconia-toughened alumina (ZTA), alumina-toughened zirconia (ATZ) and yttria-stabilized zirconia (YSZ), were tested as anvil materials, mainly for the purpose of neutron scattering study under high pressure. ZTA with non-toroidal anvil profile, having the same sample volume as conventionally used double toroidal anvils, sustained pressures up to 11.9 GPa. This is comparable to anvils made of tungsten carbide (TC) with Ni binder with the same dimensions. ATZ would also be an alternative material to TC with pressure performance comparable to ZTA, whereas YSZ is much weaker than the other two ceramics. The attenuation coefficient for YSZ is significantly smaller than that of TC and similar to ZTA and ATZ, the latter being estimated by attenuation calculations. Neutron diffraction on a sample of lead in YSZ anvils as well as quasi-elastic neutron scattering on liquid water in ZTA also demonstrate the outstanding neutron transparency of these ceramics. The gain factor in count rate is up to one order of magnitude.