Because clouds play a large role in energy transfer in the atmosphere, a substantial source of uncertainty in climate and weather modeling comes from our inability to predict when cloud droplets will become large enough to fall to Earth as rain. Cloud droplets grow quickly due to condensation when they are small, but collisions between droplets are necessary to explain the rapid onset of rain. Turbulence plays an essential role in driving cloud droplets towards collision, but it is the near-contact motion of the droplets at separation distances smaller than the smallest eddies in the turbulence that ultimately determines whether or not droplets reach contact. There is a dearth of experimental observations of the motion of cloud droplets at small separations in part because conventional particle tracking fails when particles get too close together. In this work, we study the near-contact regime of cloud droplet motion using new methods that for the first time allow us to observe the behavior of the droplets when the gap distance between them is on the order of a tenth of the droplet sizes, an order of magnitude smaller than previous experiments. In the first part of this work, we develop new experimental methods that can be integrated into the conventional steps of three-dimensional Lagrangian Particle Tracking (LPT) and test the methods on synthetic and real particle image data.We develop a new particle identification algorithm, which we name Pratt-Walking, that can accurately identify the position and size of high-resolution, circular droplet images even when they overlap by up to 80%. We also develop a new, computationally efficient tracking algorithm that produces an order of magnitude fewer tracking errors than the previous state-of-the-art Four Frame Best Estimate for all studied values of tracking difficulty. In the second part of this work, we apply our new methods to data generated by our collaborators at the University of Gothenburg:images of the near-contact motion of electrically charged and uncharged droplet pairs with radii between 17 and 27 microns as they settle through quiescent air, which is an experimental approximation of a weakly turbulent cloud. We show that the dynamical system governing the collision outcome for highly charged droplets is fundamentally different than for uncharged droplets, with edge-case collisions occurring only after the larger droplet has overtaken the smaller droplet. We also observe directly for the first time the relative acceleration of uncharged droplets as they approach collision. We find that the relative acceleration is explained by continuum hydrodynamic interactions to within the resolution of our measurements.