The detection of satellites around exoplanets, or exomoons, remains a largely unexplored territory. Searching for exomoons to constrain their occurrence rates and bulk properties is important because it can provide insights into the formation of exoplanets and circumplanetary disks and provide new places to search for habitability. Combining high resolution spectroscopy with high contrast imaging can be used to measure the radial velocities of planets directly to search for exomoons. Current instrumentation (KPIC) is sensitive to detecting moons with 1-4% the mass of its host planet and could probe gravitational instabilities as a way to create binary brown dwarfs. The next generation of high-resolution spectrographs may provide the precision necessary to perform searches for solar system-like exomoons around directly imaged planets (mass ratios of q~10^(-4)).