Atrial fibrillation (AF) is the most prevalent cardiac arrhythmia. The growing epidemic of AF already affects millions of patients around the world and millions more are forecast to develop the condition in coming decades. The standard non-pharmacological treatment for AF is catheter ablation, an invasive and time consuming procedure. Non-invasive treatment of AF with radiosurgery has recently been put forward but is challenged by complex cardiac and respiratory motion. Compensating for target motion and treating in real-time could be realised with a MRI linear accelerator (MRI-Linac). A recent study developed methodology to track cardiac targets for this purpose but until now no measure of its accuracy has been accessible. In this investigation, the existing real-time cardiac tracking is quantified and developed on a digital phantom platform. It is first tested within a perfect digital scenario and then extended to a realistic anthropomorphic simulation. In a final experiment, developed tracking methods are applied to real-world anatomical data. A total number of twenty-one virtual patients were generated with the 4 dimensional extended cardiac-torso (XCAT) phantom software and received magnetic resonance imaging (MRI) simulated cardiac scans. A 3D volume representing a distinct cardiac phase is comprised of 2D slices which cover the entire target area. These template volumes are matched through pixel similarity to 2D orthogonal real-time MRI planes to localise the target volume in real-time. One virtual patient represented ideal and thus unrealistic MRI scans to initially test the cardiac tracking. Twenty virtual patients were subjected to MRI scans that closely model the proposed real-world scenario. An available ground-truth is compared to target motion trajectories output from the cardiac tracking algorithm for the twenty-one virtual patients. The cardiac tracking methodology is simultaneously developed as a result of the quantitative measures. Additionally, the correlation and significance of the virtual patients’ physiological parameters with tracking accuracy is investigated. Finally, the best performing tracking function is qualitatively assessed on a single patient’s real-world MRI scans. Employing a tracking method with the same basic methodology as the original tracking on the twenty virtual patient cohort resulted in a mean 3D tracking error of 3.2 ± 1.7 mm. The three anatomical plane constituent errors were 1.3 ± 0.9 mm in the superior inferior (SI) plane, 1.4 ± 0.9 mm in the anterior posterior (AP) plane and 2.2 ± 1.8 mm in the left right (LR) plane. This result is in strong agreement with the inferred error of 3 - 4 mm from the previous study that was based on 2D quantification. After tracking developments were implemented, the best performing mean 3D tracking error of 2.9 ± 1.6 mm was ascertained. A patient’s heart rate is the only anatomical parameter to show a significant linear relationship with tracking error (r=0.65, p-value = 0.0018). Comparing best performing tracking functions across the virtual patients show that the optimal tracking function is patient-specific. When the developed methods were reintroduced to a patient’s MRI data the tracking accuracy was qualitatively assessed to have improved. The results of the previous single patient treatment planning indicate that high-dose cardiac radiosurgery can be administered for the treatment of AF when safety margins are below 5 mm. The quantitative measures presented here demonstrate that real-time target localisation and motion compensation could successfully be implemented with an MRI-Linac. The conclusions of this work strongly encourage further development of the proposed AF treatment with non-invasive radiosurgery.