Angular distributions have been measured for 0+ --> 1+ transitions with the (C-12, B-12) reaction on targets of C-12, Mg-26, Fe-54, Ni-58, and Zr-90 and with the (C-12, N-12) reaction on targets of C-12 and Fe-56. The bombarding energy was E/A = 70 MeV, and small-angle data were obtained. A comparison of the cross sections measured for the (C-12, B-12) reaction with the results of distorted-wave-approximation calculations indicates that 0+ --> 1+ transitions are predominantly one step at E/A = 70 MeV. The calculated cross sections are generally in good agreement (to within 40% in magnitude) with the measured cross sections, and the angular distributions are well described quantitatively in many cases. A correlation between cross sections and known Gamow-Teller (GT) strengths B(GT) for the corresponding transitions has been found. This correlation, which is weakly dependent on the target mass, establishes a calibration for the reactions. It is used to determine B(GT) values of astrophysical interest for two low-lying 1+ levels in Mn-56 from the cross sections measured for the Fe-56(C-12, N-12)Mn-56 reaction. The results are compared with two shell-model calculations performed to obtain B(GT) for Fe-56 --> Mn-56 transitions and with another calculation from the literature. Computational tests were performed to evaluate (a) the contribution to the cross sections of terms not present in nucleon-induced charge-exchange reactions and (b) the extent to which the cross sections provide a measure of GT strength.