Ruptured coronary atherosclerotic plaques commonly cause acute myocardial infarction. It has been recently shown that active microcalcification in the coronary arteries, one of the features that characterizes vulnerable plaques at risk of rupture, can be imaged using cardiac gated 18F-sodium fluoride (18F-NaF) PET. We have shown in previous work that a motion correction technique applied to cardiac-gated 18F-NaF PET images can enhance image quality and improve uptake estimates. In this study, we further investigated the applicability of different algorithms for registration of the coronary artery PET images. In particular, we aimed to compare demons vs. level-set nonlinear registration techniques applied for the correction of cardiac motion in coronary 18F-NaF PET. To this end, fifteen patients underwent 18F-NaF PET and prospective coronary CT angiography (CCTA). PET data were reconstructed in 10 ECG gated bins; subsequently these gated bins were registered using demons and level-set methods guided by the extracted coronary arteries from CCTA, to eliminate the effect of cardiac motion on PET images. Noise levels, target-to-background ratios (TBR) and global motion were compared to assess image quality. Compared to the reference standard of using only diastolic PET image (25% of the counts from PET acquisition), cardiac motion registration using either level-set or demons techniques almost halved image noise due to the use of counts from the full PET acquisition and increased TBR difference between 18F-NaF positive and negative lesions. The demons method produces smoother deformation fields, exhibiting no singularities (which reflects how physically plausible the registration deformation is), as compared to the level-set method, which presents between 4 and 8% of singularities, depending on the coronary artery considered. In conclusion, the demons method produces smoother motion fields as compared to the level-set method, with a motion that is physiologically plausible. Therefore, level-set technique will likely require additional post-processing steps. On the other hand, the observed TBR increases were the highest for the level-set technique. Further investigations of the optimal registration technique of this novel coronary PET imaging technique are warranted.