In this paper we present an experimental investigation of the nonlinear microwave properties of coplanar resonators patterned from epitaxial Y1Ba2Cu3O7-δ thin films in zero-field-cooled, field-cooled, and field-sweep experiments in the search for the fundamental limiting mechanism. The impact of magnetization, vortices, intrinsic limitation, grain boundaries, and thermal effects is evaluated. We find that the fundamental limiting mechanism in the absence of thermal and grain-boundary effects is given by the dc critical current density of the superconducting material which masks the intrinsic limitation expected at larger rf current densities. Demagnetizing effects, penetration barriers, vortex penetration, pinning, and relaxation of inhomogeneous vortex distributions are experimentally observed and in agreement with theoretical expectations. The experimental results are modeled in terms of a simple model for the power-handling capability which is based on a superposition of all current densities in the resonator and gives a consistent explanation of all experiments in magnetic fields and in zero field.