Cardiac T1 maps rely upon the acquisition of spatially aligned images. When patients fail to maintain breath hold, respiratory motion can cause T1 map inaccuracies due to poor image alignment. In the method demonstrated here, images are registered by co-registration to synthetic images, which are created via a non-iterative, automatic, model-based method. This method is compared to an iterative registration method using an energy minimisation process for quantitative registration accuracy and speed. Both methods were found to significantly improve image registration. The resultant registrations from both methods did not significantly differ, however the non-iterative model-based method reduced processing time by 1/5th.