Performing rheo-microMRI velocimetry at a high magnetic field with strong pulsed field gradients has clear advantages in terms of (chemical) sensitivity and resolution in velocities, time, and space. To benefit from these advantages, some artifacts need to be minimized. Significant sources of such artifacts are chemical shift dispersion due to the high magnetic field, eddy currents caused by the pulsed magnetic field gradients, and possible mechanical instabilities in concentric cylinder (CC) rheo-cells. These, in particular, hamper quantitative assessment of spatially resolved velocity profiles needed to construct local flow curves (LFCs) in CC geometries with millimeter gap sizes. A major improvement was achieved by chemical shift selective suppression of signals that are spectroscopically different from the signal of interest. By also accounting for imperfections in pulsed field gradients, LFCs were obtained that were virtually free of artifacts. The approach to obtain quantitative LFCs in millimeter gap CC rheo-MRI cells was validated for Newtonian and simple yield stress fluids, which both showed quantitative agreement between local and global flow curves. No systematic effects of gap size and rotational velocity on the viscosity of a Newtonian fluid and yield stress of a complex fluid could be observed. The acquisition of LFCs during heterogeneous and transient flow of fat crystal dispersion demonstrated that local constitutive laws can be assessed by rheo-microMRI at a high magnetic field in a noninvasive, quantitative, and real-time manner.