Quantitative Magnetic Resonance Imaging (qMRI) extends the utility of MRI by providing reproducible indices that reflect underlying physiology as well as pathophysiology. However, qMRI is limited by long acquisition times. MR Compressed Sensing (CS) is an approach to reduce acquisition times by random undersampling of k-space coupled with a non-linear reconstruction that exploits image sparsity in some transform domain. CS provides a robust way to reduce scan times for both MRI and qMRI. We report simulation studies to explore compressed sensing for two qMRI techniques: magnetization transfer saturation (MTsat) applied to skeletal muscle and variable flip angle (VFA) spin-lattice relaxation (T1) mapping applied to the brain. The lower leg was imaged using a combination of coils (total of 8 channels) at 3T. Three fully sampled k-space data sets were acquired on the calf muscle using 3DFLASH sequences to enable MTsat calculations. The brain was imaged using a combination of head coils (total of 32 channels) at 3T. Seven fully sampled k-space data sets were acquired on the brain using 3DFLASH sequences to enable VFA T1 calculations. Simulation was performed along the phase and slice encode directions using 2D variable density Poisson disk undersampling. To evaluate CS strategies, we performed simulations on the full k-space acquisitions to determine the acceleration factors possible without degradation of image quality that also maintained the accuracy of the qMRI parameters. We also investigated the CS parameters of kernel size, mask type, and wavelet type to determine an optimized protocol for CS T1 mapping of the brain. CS reconstruction was performed using the publicly available algorithm ESPIRiT (https://mrirecon.github.io/bart/). Reconstruction was performed in 2D by taking the inverse Fourier Transform along the readout direction (kx, fully sampled) and then undersampling the ky-kz space. We found that for MTsat mapping, the highest CS acceleration factor reached was 8 to generate images with no visible artifacts and qMR values close to that from the full k-space acquisition. For the brain T1 mapping, artifact free images were reconstructed using CS acceleration values up to 64, where quantitative T1 values were also preserved.