In a method and magnetic resonance (MR) apparatus for determining a fraction of scar tissue in the myocardium of an examination person, magnetization of nuclear spins is prepared by radiation of a preparation pulse in the myocardium, and MR signals are acquired for multiple MR images while the magnetization returns to equilibrium. The multiple MR images are brought into registration with each other, so a movement of the heart between MR images is compensated. T1 times are determined using this sequence of compensated MR images. Different MR template images with different contrasts are calculated at different times after radiation of the preparation pulse, using the calculated T1 times. A myocardial contour is determined using one of the template images that has a first contrast. Scar tissue in the myocardium is determined using another template image that has a second contrast that differs from the first contrast.