Purpose: To implement a navigator-gated free-breathing 2D radial joint T1–T2 mapping technique for the myocardium at 3T, and to characterize the impact of the navigator rejection on the precision and accuracy of the T1 and T2 maps. Methods: The proposed technique, named PARMANav (for PArametric Radial Mapping with Navigator gating), collects 25 lung–liver navigator-gated electrocardiogram (ECG)-triggered single-shot radial gradient-recalled echo (GRE) images with five magnetization preparations. Source images were reconstructed using compressed sensing. Extended-phase-graph simulations were used to generate an acquisition-specific joint T1–T2 dictionary. The impact of the number of rejected navigators on the relaxation times was assessed in numerical simulations. The influence of the navigator acceptance window width (NAWW) and heart rate on the relaxation times was assessed in phantom studies, 10 healthy volunteers, and 3 patients. The relaxation times were compared to routine T1 and T2 mapping values. Results: The numerical simulations showed negligible dependence on the number of rejected navigators (