Objective. To provide 3D high-resolution cardiac T1 maps using model-based super-resolution reconstruction (SRR). Approach. Due to signal-to-noise ratio limitations and the motion of the heart during imaging, often 2D T1 maps with only low through-plane resolution (i.e. slice thickness of 6–8 mm) can be obtained. Here, a model-based SRR approach is presented, which combines multiple stacks of 2D acquisitions with 6–8 mm slice thickness and generates 3D high-resolution T1 maps with a slice thickness of 1.5–2 mm. Every stack was acquired in a different breath hold (BH) and any misalignment between BH was corrected retrospectively. The novelty of the proposed approach is the BH correction and the application of model-based SRR on cardiac T1 Mapping. The proposed approach was evaluated in numerical simulations and phantom experiments and demonstrated in four healthy subjects. Main results. Alignment of BH states was essential for SRR even in healthy volunteers. In simulations, respiratory motion could be estimated with an RMS error of 0.18 ± 0.28 mm. SRR improved the visualization of small structures. High accuracy and precision (average standard deviation of 69.62 ms) of the T1 values was ensured by SRR while the detectability of small structures increased by 40%. Significance. The proposed SRR approach provided T1 maps with high in-plane and high through-plane resolution (1.3 × 1.3 × 1.5–2 mm3). The approach led to improvements in the visualization of small structures and precise T1 values.