Collision strengths for the low-energy scattering of electrons by Fe XXIII and Fe VII have been calculated using the Dirac R-matrix method. For Fe XXIII the results for the excitation from the ground state (1s²2s²)¹S^e₀ to the third level (1s²2s2p) ³P^o₁ have been compared with earlier Breit-Pauli and non-relativistic calculations. The agreement is found to be good as expected since relativistic effects are important but not dominant. For Fe VII, excitations between the first nine levels have been considered and a comparison made with an earlier distorted-wave calculation. These are both extensive tests of the method and demonstrate that it can be used to produce reliable electron-ion collision data.