Myocardial T1-mapping bears promise for evaluation of numerous cardiomyopathies, but requires multiple breath-hold scans with conventional techniques. In this study we explored the acceleration potential of multi-band imaging for myocardial SAPPHIRE T1-mapping with 3-slice coverage in a single breath-hold. Three linear methods for slice and in-plane unaliasing were evaluated. Phantom studies confirmed the accuracy of the proposed T1-mapping method, and in-vivo evaluation has shown reliable image quality with 3-fold acceleration at the cost of 1.3 to 1.7-fold increased in-vivo variability. Smaller loss in-vivo precision was achieved using regularized methods, for the trade-off against increased inter-slice leakage.