Stability and phase transformations in the high-pressure-synthesized phases of FeGe and MnGe with a noncentrosymmetric B20-type crystal structure are studied theoretically using ab initio density-functional calculations and experimentally by means of differential scanning calorimetry. For both germanides in magnetic state, the evolutionary genetic search yields the same set of preferred equiatomic polymorphs. In case of FeGe, this result is consistent with available theoretical and experimental information, whereas for MnGe we find new hypothetical phases, in addition to the known metastable B20 phase. The ground state of nonmagnetic MnGe is unexpectedly represented by a tetragonal structure quite unusual for the pd-bonded AB-type compounds. It follows from our calculations that, for a given input chemical composition, the existence of a structure stable at finite temperatures (and pressures) can be efficiently established by zero-temperature evolutionary search, if this structure appears in the output short list of lowest-energy states. The presented calorimetric study of the metastable FeGe and MnGe phases shows that their behavior upon heating notably depends on preparation method and sample history.