Charm and charmonium physics have gained renewed interest in the past decade. Recent spectroscopic observations strongly motivate these studies. Among the several possible reactions, measurements in proton-antiproton annihilation play an important role, complementary to the studies performed at B-factories. The fixed target PANDA experiment at FAIR (Darmstadt, Germany) will investigate fundamental questions of hadron and nuclear physics in the interactions of antiprotons with nucleons and nuclei. With reaction rates as large as 2*10^7 interactions/s, and a mass resolution 20 times better as compared with the most recent B-factories, PANDA is in a privileged position to successfully perform the measurement of the width of narrow states, such as the X(3872). PANDA will investigate also high spin particles, whose observation was forbidden at B-factories, i.e. F-wave charmonium states. In this report extrapolations on cross sections and rates with PANDA are given.