The Penning trap REXTRAP at ISOLDE was used to test the feasibility of in-trap conversion electron spectroscopy. The results of simulations, experiments with solid conversion electron sources as well as first on-line tests with trapped radioactive ions are presented. In addition to obtaining high-resolution spectroscopic data, the detection of conversion electrons was found to be a useful tool for the diagnostics of the trap operation. The tests proved the feasibility of in-trap spectroscopy but also revealed some potential problems to be addressed in the future.