In search for new magnetic materials, we make computer prediction of structural, electronic and magnetic properties of yet-to-be synthesized Rh-based double perovskite compounds, Sr(Ca) 2 BRhO 6 (B=Cr, Mn, Fe). We use combination of evolutionary algorithm, density functional theory, and statistical-mechanical tool for this purpose. We find that the unusual valence of Rh 5+ may be stabilized in these compounds through formation of oxygen ligand hole. Interestingly, while the Cr-Rh and Mn-Rh compounds are predicted to be ferromagnetic half-metals, the Fe-Rh compounds are found to be rare examples of antiferromagnetic and metallic transition-metal oxide with three-dimensional electronic structure. The computed magnetic transition temperatures of the predicted compounds, obtained from finite temperature Monte Carlo study of the first principles-derived model Hamiltonian, are found to be reasonably high. The prediction of favorable growth condition of the compounds, reported in our study, obtained through extensive thermodynamic analysis should be useful for future synthesize of this interesting class of materials with intriguing properties.