We present a novel method for estimating respiratory motion using inertial measurement units (IMUs) based on microelectromechanical systems (MEMS) technology. As an application of the method we consider the amplitude gating of positron emission tomography (PET) imaging, and compare the method against a clinically used respiration motion estimation technique. The presented method can be used to detect respiratory cycles and estimate their lengths with state-of-the-art accuracy when compared to other IMU-based methods, and is the first based on commercial MEMS devices, which can estimate quantitatively both the magnitude and the phase of respiratory motion from the abdomen and chest regions. For the considered test group consisting of eight subjects with acute myocardial infarction, our method achieved the absolute breathing rate error per minute of 0.44 +/- 0.23 1/min, and the absolute amplitude error of 0.24 +/- 0.09 cm, when compared to the clinically used respiratory motion estimation technique. The presented method could be used to simplify the logistics related to respiratory motion estimation in PET imaging studies, and also to enable multi-position motion measurements for advanced organ motion estimation.