Respiratory motion during myocardial perfusion imaging can cause artefacts in both positron emission tomography (PET) and single-photon emission computed tomography (SPECT) images when mismatches between emission and transmission datasets arise. In this study, artefacts from different breathing motions were quantified in both modalities to assess key factors in attenuation-correction accuracy. Activity maps were generated using the NURBS-based cardiac-torso phantom for different respiratory cycles, which were projected, attenuation-corrected and reconstructed to form PET and SPECT images. Attenuation-correction was performed with maps at mismatched respiratory phases to observe the effect on the left-ventricular myocardium. Myocardial non-uniformity was assessed in terms of the standard deviation in scores obtained from the 17-segment model and changes in uniformity were compared for each mismatch and modality. Certain types of mismatch led to artefacts and corresponding increases in the myocardial non-uniformity. For each mismatch in PET, the increases in non-uniformity relative to an artefact-free image were as follows: (a) cardiac translation mismatch, 84% +/- 11%; (b) liver mismatch, 59% +/- 10%, (c) lung mismatch from diaphragm contraction, 28% +/- 8%; and (d) lung mismatch from chest-wall motion, 6% +/- 7%. The corresponding factors for SPECT were (a) 61% +/- 8%, (b) 34% +/- 8%, (c) -2% +/- 7)% and (d) -4% +/- 6%. Attenuation-correction artefacts were seen in PET and SPECT images, with PET being more severely affected. The most severe artefacts were produced from mismatches in cardiac and liver position, whereas lung mismatches were less critical. Both cardiac and liver positions must, therefore, be correctly matched during attenuation correction.