Magnetic resonance elastography (MRE) is a non-invasive phase-contrast-based method for quantifying the shear stiffness of biological tissues. Synchronous application of a shear wave source and motion encoding gradient waveforms within the MRE pulse sequence enable visualization of the propagating shear wave throughout the medium under investigation. Encoded shear wave-induced displacements are then processed to calculate the local shear stiffness of each voxel. An important consideration in local shear stiffness estimates is that the algorithms employed typically calculate shear stiffness using relatively high signal-to-noise ratio (SNR) MRE images and have difficulties at an extremely low SNR. A new method of estimating shear stiffness based on the principal spatial frequency of the shear wave displacement map is presented. Finite element simulations were performed to assess the relative insensitivity of this approach to decreases in SNR. Additionally, ex vivo experiments were conducted on normal rat lungs to assess the robustness of this approach in low SNR biological tissue. Simulation and experimental results indicate that calculation of shear stiffness by the principal frequency method is less sensitive to extremely low SNR than previously reported MRE inversion methods but at the expense of loss of spatial information within the region of interest from which the principal frequency estimate is derived.