Phase contrast magnetic resonance imaging (PC-MRI) is subject to numerous sources of error, which decrease clinical confidence in the reported measures. This work outlines how stationary perivascular fat can impart a significant chemical shift induced PC-MRI measurement error using computational simulations, in vitro, and in vivo experiments. This chemical shift error does not subtract in phase difference processing, but can be minimized with proper parameter selection. The chemical shift induced phase errors largely depend on both the receiver bandwidth (BW) and the TE. Both theory and an in vivo comparison of the maximum difference in net forward flow between vessels with and without perivascular fat indicated that the effects of chemically shifted perivascular fat are minimized by the use of high BW (814 Hz/px) and an in-phase TE (HBW-TEIN). In healthy volunteers (N=10) HBW-TEIN significantly improves intrapatient net forward flow agreement compared to low BW (401 Hz/px) and a mid-phase TE as indicated by significantly decreased measurement biases and limits of agreement for the ascending aorta (1.8±0.5 mL vs. 6.4±2.8 mL, P=0.01), main pulmonary artery (2.0±0.9 mL vs. 11.9±5.8 mL, P=0.04), the left pulmonary artery (1.3±0.9 mL vs. 5.4±2.5 mL, P=0.003), and all vessels (1.7±0.8 mL vs. 7.2±4.4 mL, P=0.001).