Purpose: To develop a respiratory-resolved motion-compensation method for free-breathing, high-resolution coronary magnetic resonance angiography using a 3D cones trajectory. Methods: To achieve respiratory-resolved 0.98 mm resolution images in a clinically relevant scan time, we undersample the imaging data with a variable-density 3D cones trajectory. For retrospective motion compensation, translational estimates from 3D image-based navigators (3D iNAVs) are used to bin the imaging data into four phases from end-expiration to end-inspiration. To ensure pseudo-random undersampling within each respiratory phase, we devise a phyllotaxis readout ordering scheme mindful of eddy current artifacts in steady state free precession imaging. Following binning, residual 3D translational motion within each phase is computed using the 3D iNAVs and corrected for in the imaging data. The noise-like aliasing characteristic of the combined phyllotaxis and cones sampling pattern is leveraged in a compressed sensing reconstruction with spatial and temporal regularization to reduce aliasing in each of the respiratory phases. Results: In a volunteer and 5 patients, respiratory motion compensation using the proposed method yields improved image quality compared to non-respiratory-resolved approaches with no motion correction and with 3D translational correction. Qualitative assessment by two cardiologists indicates the superior sharpness of coronary segments reconstructed with the proposed method (P < 0.01). Conclusion: The proposed method better mitigates motion artifacts in free-breathing, high-resolution coronary angiography exams compared to translational correction.