Cryogenic Penning traps have proven to be a powerful tool for probing the boundary of validity of our standard model of physics by comparing precise measurements with theory predictions. Such traps allow suspending a wide range of ions and particles - including highly charged ions and antimatter - in free space, protected from uncontrolled interactions with the environment. Then, their motional frequencies in the magnetic field of the trap as well as their internal quantum state and specifically spin precession frequencies can be measured precisely. The ultra-precise determination of the g-factor of highly charged ions with the ALPHATRAP experiment at MPIK for example allows testing the validity of quantum electrodynamics (QED) in strong electric fields, ranging up to an extreme $10^{16}$~V/cm in the case of hydrogenlike lead $^{208}$Pb$^{81+}$ . Furthermore, the new LSym (Lepton Symmetry Experiment) project will search for a possible violation of CPT (charge-parity-time reversal) symmetry, indicated by an asymmetry between matter and antimatter, by crystalising a single positron and an electron and comparing their properties with orders of magnitude higher precision than previously possible. I will introduce cryogenic Penning traps and our toolbox and present our recent experiments.