Context. Recent high angular resolution polarimetric continuum observations of circumstellar disks provide new insights into their magnetic field. However, direct constraints are limited to the plane-of-sky component of the magnetic field. Observations of Zeeman split spectral lines are a potential way to enhance these insights by providing complementary information. Aims. We investigate which constraints for magnetic fields in circumstellar disks can be obtained from Zeeman observations of the 113 GHz CN lines. Furthermore, we analyze the conditions needed to perform these observations and their dependence on selected quantities. Methods. We simulate the Zeeman splitting with the radiative transfer (RT) code POLARIS extended by our Zeeman splitting RT extension ZRAD, which is based on the line RT code Mol3D. Results. We find that Zeeman observations of the 113 GHz CN lines provide significant insights into the magnetic fields of circumstellar disks. However, with the capabilities of recent and upcoming instruments and observatories, even spatially unresolved observations would be challenging. Nevertheless, these observations are feasible for the most massive disks with a strong magnetic field and high abundance of CN/H. The most restrictive quantity is the magnetic field strength, which should be at least on the order of ∼1 mG. In addition, the inclination of the disk should be around 60• to preserve the ability to derive the line-of-sight (LOS) magnetic field strength and to obtain a sufficiently high circularly polarized flux. Finally, we simulate the RT of a circumbinary disk model based on a magnetohydrodynamic (MHD) simulation. We find that our analysis of the magnetic field is still applicable. However, owing to their lower circularly polarized emission, Zeeman observations of circumbinary disks with a significant separation between their stellar components (r star ∼ 10 AU) are more challenging than observations of circumstellar disks with a single star.