We study the influence of a tunnel barrier on the quantum transport through a circular cavity. Our analysis in terms of classical trajectories shows that the semiclassical approaches developed for ballistic transport can be adapted to deal with the case where tunneling is present. Peaks in the Fourier transform of the energy-dependent transmission and reflection spectra exhibit a nonmonotonic behaviour as a function of the barrier height in the quantum mechanical numerical calculations. Semiclassical analysis provides a simple qualitative explanation of this behaviour, as well as a quantitative agreement with the exact calculations. The experimental relevance of the classical trajectories in mesoscopic and microwave systems is discussed.