The subject of this thesis is high-precision mass-measurements performed with Penning trap mass spectrometers (PTMS). In particular it describes the SMILETRAP I PTMS and the final results obtained with it, the masses of 40Ca and that of the proton. The mass of 40Ca is an indispensible input in the evaluation of measurements of the bound electron g-factor, used to test quantum electrodynamical calculations in strong fields. The value obtained agrees with available literature values but has a ten times higher precision. The measurement of the proton mass, considered a fundamental physical constant, was performed with the aim of validating other Penning trap results and to test the limit of SMILETRAP I. It was also anticipated that a measurement at a relative precision close to 10-10 would give insight in how to treat certain systematic uncertainties. The result is a value of the proton mass in agreement with earlier measurements and with an unprecedented precision of 1.8×10-10. Vital for the achieved precision of the proton mass measurement was the use of the Ramsey excitation technique. This technique, how it was implemented at SMILETRAP I and the benefits from it is discussed in the thesis and in one of the included papers. The second part of the thesis describes the improved SMILETRAP II setup at the S-EBIT laboratory, AlbaNova. All major changes and upgrades compared to SMILETRAP I are discussed. This includes, apart from the Ramsey excitation technique, higher ionic charge states, improved temperature stabilization, longer run times, different reference ions, stronger and more stable magnetic field and a more efficient ion detection. Altogether these changes should reduce the uncertainty in future mass determinations by an order of magnitude, possibly down to 10-11. / At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 9: Accepted.