Artifacts due to off-resonance effects are a significant challenge for non-Cartesian MRI. In FISP-based MRF sequences, if the entire spiral readout is employed to generate a highly undersampled image, any off-resonance during the readout will lead to blurring. However, short portions of the readout will be mostly free of dephasing due to off-resonance effects. By gridding only segments of the readout, it may be possible to quantify the resonance frequency along with T1 and T2. This work shows a proof-of-principle application of this idea using the cardiac MRF sequence with the rosette trajectory in simulations.