In a method and magnetic resonance apparatus to acquire and present calibration images of a periodically moving organ with the use of magnetic resonance technology, calibration images are acquired by acquiring measurement data for multiple calibration images during one continuous period of the organ movement, the multiple calibration images differing in their offset frequency and/or in their spatial position in the organ to be examined, and the calibration images in a presentation manner that, from the visual quality of the respective images, allows the user to select (identify) the image acquired with the offset frequency that should then be used to acquire the diagnostic image are displayed to a user.