Black Hole Masses Across Cosmic Time: Precise Measurements Using Strong Gravitational Lensing and Reverberation Mapping Data

There is overwhelming evidence for a link between supermassive black holes (BHs) and their host galaxies, yet the physical mechanisms behind the connection are poorly understood. Discerning between possible co-evolutionary scenarios requires precise measurements of BH masses and host properties across cosmic time. BH mass measurements outside the local universe require bright active galactic nuclei (AGNs), but the AGN light overwhelms the light of the host, making host property measurements difficult. Further, BH mass estimates rely on the unresolvable broad emission line region (BLR), and the unknown nature of the BLR limits their precision.In this dissertation, I use a unique combination of gravitational lensing and reverberation mapping techniques to tackle both issues. First, I present a semi-supervised classification approach for identifying rare lensed quasars based solely on photometry in wide-field surveys. Lenses are powerful tools for measuring host properties, but studies are limited by the small sample size, so discovery efforts are crucial. Using this technique, I successfully discovered three new lenses in the Sloan Digital Sky Survey, with several other candidates awaiting further follow-up. This approach is flexible and can easily be modified to target specific types of lenses as well as lenses in surveys covering different portions of the sky.Next, I use a modeling framework to measure precise BH masses for seven AGNs and infer the structural and kinematic properties of the Hβ BLR. This nearly doubles the sample size of modeled BLRs, allowing for a correlation analysis between BLR properties and AGN observables that can be used to improve BH mass measurements for all AGNs. I then model Hβ, CIV, and Lyα in NGC 5548 using data from 85 Hubble Space Telescope orbits and multiple ground-based telescopes to understand the similarities and differences between the optical and UV BLRs. High-z BH mass measurements rely on UV lines, but our current understanding of the UV BLR is severely lacking, so understanding their connection is critical for decreasing high-z BH mass uncertainties. Finally, I tie the previous projects together with the most precise high-z BH mass measurement to date, using data from a 4.5 year monitoring campaign of a strongly lensed quasar at z=2.805. Accounting for gravitational time delays, the campaign exceeds 6 years in duration. Understanding the co-evolution of BHs and their hosts will require measurements of this precision at high-z, and this research demonstrates that gravitational lensing makes this level of precision obtainable