Measuring the internal quality factor of coplanar waveguide superconducting resonators is an established method of determining small losses in superconducting devices. Traditionally, the resonator losses are only attributed to two-level system (TLS) defects using a power dependent model for the quality factor. However, excess non-equilibrium quasiparticles can also limit the quality factor of the planar superconducting resonators used in circuit quantum electrodynamics. At millikelvin temperatures, quasiparticles can be generated by breaking Cooper pairs via high-energy particles or sub-gap microwave photons from the measurement signal.In this thesis, I developed a two-temperature, power, and temperature dependent model to evaluate resonator losses for isolating TLS and quasiparticle loss simultaneously. The model combines a standard TLS model with a new modified two-temperature quasiparticle model where the driven quasiparticle density is defined by an effective temperature that may be different than the bath temperature. This model also explores the power and temperature dependence of the internal quality factor. To investigate the model, resonators were fabricated from epitaxial molecular beam epitaxy-grown aluminum and titanium nitride grown on float-zone refined silicon. The resonators have high-quality factors above 1M. The presented model is used to determine that the analyzed TiN resonator had comparable TLS and quasiparticle loss at low power and low temperature, while the low-temperature Al resonator behavior was dominated by non-equilibrium quasiparticle loss. Additionally, a small bandgap superconductor in contact with a larger bandgap superconductor as a quasiparticle trap is also explored. The quasiparticles can be confined away from the larger bandgap superconductor into the smaller one. Here, Al and TiN were used as two superconductors. Finite difference method (FDM) simulations of the coupled phonon and quasiparticle systems of both superconductors are performed, suggesting that the quasiparticle traps on the ground plane may be effective for setback distances less than 200 μm away from TiN waveguide features. Experimentally, a thin layer of Al is grown in-situ on TiN using molecular beam epitaxy (MBE) with a negligible dielectric layer between the two superconductors to increase the trapping efficiency of the Al. The quarter-wavelength resonators in TiN with an Al layer with varying setback distances (1 µm – 150 µm) from the active region of the TiN were also fabricated using custom-designed mask sets. These devices are then analyzed for different powers and temperatures. The resonators with setback greater than 20 µm outperform the plain TiN resonators at low temperatures. The device with a setback of 150 µm had 1.5x the quality factor at medium powers at low temperatures.