The polarization of C-13 nuclei by means of nuclear orientation via electron spin-locking (Hartmann-Hahn cross-polarization between paramagnetic electrons and C-13 nuclei) in a suite of natural diamonds has been investigated at 2.4 GHz and 9.6 GHz. The C-13 polarization rate has been found to be independent of the microwave frequency, in agreement with theory. It is shown that since T-1 rho(e) much less than T-1(e) for diamond, the effective polarization rate of C-13 nuclei is relatively low. At low paramagnetic impurities (C-e < 5 ppm) C-13 nuclei in diamond are polarized faster by employing continuous wave microwave radiation to drive the forbidden transitions of the C-13-electron spin system, the so-called solid effect.