The novel Penning-trap mass spectrometer PENTATRAP aims at mass-ratio determinations of medium-heavy to heavy ions with relative uncertainties below 10−11. From the mass ratios of certain ion species, the corresponding mass differences will be determined with sub-eV/c2uncertainties. These mass differences are relevant for neutrino-mass experiments, a test of special relativity and tests of bound-state QED. Means to obtain the required precision are very stable trapping fields, the use of highly-charged ions produced by EBITs, a non-destructive cyclotron-frequency determination scheme employing detectors with single-ion sensitivity and a five-trap tower, that allows for measurement schemes being insensitive to magnetic field drifts. Within this thesis, part of the detection electronics was set up and tested under experimental conditions. A single-trap setup was realized. A Faraday cup in the trap tower enabled the proper adjustment of the settings of the beamline connecting the EBIT and the Penning-trap system, resulting in the first trapping of ions at PENTATRAP. A stabilization of switched voltages in the beamline and detailed studies of ion bunch characteristics allowed for reproducible loading of only a few ions. Detection of the axial oscillation of the trapped ions gave hints that in some cases, even single ions had been trapped. Furthermore, valuable conclusions about necessary modifications of the setup could be drawn