We describe recent advances in developing radiation-hard ceramic resistive plate chambers (CRPCs) with Si3N4/SiC composites. Bulk resistivity measurements for this material for different manufacturing processes are reported. The results show that the bulk resistivity ρ can vary between 107and1013Ωcm. The varistor type behaviour of the material is analysed. A comparison with other materials used in timing RPCs is given. We describe the assembly and tests of CRPC prototypes in electron and proton beams. For a prototype with ρ~5×109Ωcm, the efficiency of the detectors is 95% at a flux of 2×105cm−2s−1. The time resolution at the same flux is about 120ps. A prototype with ρ~2×1010Ωcm shows an efficiency of about 85% up to fluxes of 5×104cm−2s−1 with a time resolution better than 80ps. The results are compared with RPC models.