Electron spin resonance (ESR) spectroscopy has been extensively used to study structure and dynamics in proteins and lipids. ESR has been shown to be sensitive to a wide range of molecular motions with time scales ranging from tens of nanoseconds to microseconds. In particular, two-dimensional electron–electron double resonance (2D-ELDOR) provides extensive insight into molecular motions. Recent developments permitting experiments at higher frequencies (95 GHz) provide molecular orientational resolution, enabling a clearer description of the nature of the motions. However, we find that the existing theoretical methods for computing 2D-ELDOR experiments over a wide motional range begin to fail seriously when applied to very slow motions characteristic of proteins in solution. One reason is the failure to obtain accurate eigenvectors and eigenvalues of the complex symmetric stochastic Liouville matrices describing the experiment when computed by the efficient Lanczos algorithm in the range of very slow motion. Another, perhaps more serious, issue is that these matrices are “non-normal,” such that for the very slow motional range even rigorous diagonalization algorithms do not yield the correct eigenvalues and eigenvectors. We have employed algorithms that overcome both these issues and lead to valid 2D-ELDOR predictions even for motions approaching the rigid limit. They are utilized to describe the development of cross-peaks in 2D-ELDOR at 95 GHz for a particular case of domain motion. In order to perform these simulations, it was found that the standard approach of solving the relevant stochastic Liouville equation using the efficient Lanczos algorithm for this case breaks down, so algorithms were employed that rely on the Arnoldi iteration. While they lead to accurate simulations, they are very time-consuming. In this work, we focus on a variant known as the rational Arnoldi algorithm. We show that this can achieve a significant reduction in computation time. A method of adaptive shift choice is introduced to optimize this selection. We also find that these procedures help in optimizing the pruning procedure that greatly reduces thedimension of the initial N dimensional stochastic Liouville matrix in such subsequent computations. We also consider the case of CW saturation spectroscopy and show the applicability of our approach to fit CW saturation spectra. All these studies show the power of ESR in revealing microsecond-scale dynamics in biological systems. Chapters 2, 3, and 4 have been published in the following peer-reviewed research articles respectively: P. Gupta, Z. Liang, and J. H. Freed. J. Chem. Phys., 152:214112, 2020, P. Gupta, K. Chaudhuri, and J. H. Freed. J. Chem. Phys., 154:084115, 2021, and P. Gupta, B. Dzikovski, and J. H. Freed. Appl. Magn. Reson., accepted July 2021.