As data rates are driven faster and with the millimeter-wave frequencies of 5G cellular communications, the characterization of dielectric materials and packaging at these frequencies becomes essential. The characterization discussed here is the complex permittivity at microwave and millimeter-wave frequencies. The complex permittivity is commonly described by the dielectric constant and loss tangent of a dielectric. Extraction of the material permittivity can be a laborious process. Some methodologies include using rectangular cavity resonators, substrate integrated waveguide resonators, ring resonators, split-post resonators, split-cylinder resonators, differential length transmission lines, and other cavity perturbation methods. There is a need to improve and simplify the process of material characterization at microwave and millimeter-wave frequencies. There is not much in the way of published work on flip-chip underfill characterization, especially at microwave and millimeter-wave frequencies. Solid walled cavity resonators are used here to characterize flip-chip underfill. The underfill, typically an epoxy resin based material, offers thermal and structural benefits for the integrated circuit (IC) on package. With many interconnects in close proximity to one another, the integrated circuits on package can have unexpected signal and power integrity issues if the electrical characteristics of the underfill material are not known and not accounted for. The characterization methodologies focused on here are the dielectric-filled rectangular cavity resonator method and the substrate integrated waveguide resonator method. Dielectric characterization with these resonators is accomplished by taking measurements using a vector network analyzer (VNA) then modeling and simulating them in a full-wave simulator. Then, the measurement and simulation are overlaid, and the parameters of the dielectric are iteratively changed until a good match is seen between measurement and simulation. This resonator and full-wave simulation methodology is extended to simulations performed in a fast plane solver, where the dielectric parameters can be extracted in seconds. Also, a new approach is introduced using neural networks to predict the dielectric constant and loss tangent given a rectangular cavity resonator’s resonance frequency and the transfer impedance. These two new methodologies will work for both substrate integrated waveguide resonators and rectangular cavity resonators.