Nuclear magnetic resonance (NMR) is a powerful chemometric method for any scientist because it is easily translated to a portable format. Recent advances have made portable NMR spectroscopy economically and practically feasible. Here, the foundational physics of spin dynamics is discussed as a bridge from the abstract theory of NMR to practical applications of low field relaxometry. Relaxometry can provide a window into the molecular dynamics of a system through measurement of spin relaxation rates, which directly relate to chemical interactions and mobility within a system.The ease with which it can be customized makes portable NMR an extremely desirable technique for non-destructive, quantitative chemical analysis. However, portable NMR obtains a weaker signal with decreased resolution compared to traditional NMR. This is because spin states are not strongly split in low magnetic fields and are therefore populated nearly equally at thermodynamic equilibrium, causing weak longitudinal magnetization. As such, one typically measures exponential decay constants at low field rather than frequencies. Filtering and data analysis are considered with the development of the matrix pencil method (or MPM, so named after the mathematical entity which it employs) as a tool to aid in studies of low signal-to-noise systems and complex materials. Here, the MPM is explored first as a filtering strategy, and second, as a stable, reproducible data processing method in low field NMR. Currently, the inverse Laplace transform (ILT) is the conventional method for processing data in low field NMR. However, the ILT is hindered by sensitivity to noise, poor resolution, and high computational requirements that make it difficult to apply in non-laboratory environments. Improving the efficiency of data processing could expand the applications of portable NMR and enhance the quality of information gained from correlation experiments. The MPM fits in a broad category of filter diagonalization methods for digital signal analysis, and was developed for use in radar, antenna, and acoustics technologies. The success of the MPM in other areas of signal processing makes its application to low field NMR promising. The latter half of this dissertation describes some applications of portable NMR by coupling hardware innovations with a creative data processing strategy. First, a hospital-based measurement of blood plasma water content is developed. Next, factory-based analysis of rheological properties is presented. Finally, the use of portable high-field NMR is established for metabolomic-type assays in agricultural and environmental studies.