Microwave superconducting quantum circuits are strongly affected by various defects that are unavoidable during the production process. This paper presents a new method for measuring losses in an open transmission line. This line interacts through a capacitive coupling with a coplanar quarter-wavelength resonator, which is used to study losses therein. The authors have investigated the dependencies of losses on power and temperature (in the millikelvin range). It has been shown that major losses in a transmission line are due to the interaction of a microwave field with defects which are effectively described by two-level systems.