Collision strengths for the electron-impact excitation of forbidden transitions between 136 terms arising from 3d6, 3d54s and 3d54p configurations of Co3+ have been calculated using the R-matrix method. The accuracy of a series of models for the target terms was considered, which form the basis for R-matrix collision calculations. The importance of including configuration interaction wave functions both in the target-state expansion and in the (N+1)-electron quadratically integrable function expansion is discussed. Collision strengths were calculated for incident electron energies up to 6 Ryd. These results are believed to be the first such values for this system and will be important for plasma modelling.