The Breit-Pauli R-matrix method developed under the Iron Project has been used to obtain extensive sets of oscillator strengths and transition probabilities for dipole allowed and intercombination fine structure transitions in carbon like ions, Ar XIII and Fe XXI. The complete set consists of 1274 fine structure bound energy levels and 198259 oscillator strengths for Ar XIII, and 1611 bound levels and 300079 oscillator strengths for Fe XXI. These correspond to levels of total angular momenta of 0<=J<=7 of even and odd parities formed from total spin of 2S+1=5, 3, 1, and orbital angular momenta 0<=L<=9 with n<=10, 0<=l<=9 for each ion. The relativistic effects are included in the Breit-Pauli approximation. The close coupling wavefunction expansion for each ion is represented by the lowest 15 fine structure levels of target configurations, 2s^2^2p, 2s2p^2^ and 2p^3^. The energy levels are identified spectroscopically using a newly developed identification procedure. The procedure also makes a correspondence between the fine structure energy levels and LS terms. This provides the check for completeness of the calculated levels. Comparison is made of the present energies and the f-values with the available observed and theoretical values. Present transition probabilities agree very well with the relativistic atomic structure calculations of Mendoza et al. for the intercombination transitions, 2s2p^3^(^5^S{deg}2) - 2s^2^2p^2^(^3^P_1,2_,^1^D_2_). This further indicates that the importance of the neglected Breit interaction decreases with ion charge and constrains the uncertainty in the present calculations to within 15% even for the weak transitions.