In vacuo cryogenic environments are ideal for applications requiring both low temperatures and extremely low particle densities. This enables reaching long storage and coherence times, for example, in ion traps, essential requirements for experiments with highly charged ions, quantum computation, and optical clocks. We have developed a novel cryostat continuously refrigerated with a pulse-tube cryocooler and providing the lowest vibration level reported for such a closed-cycle system with 1 W cooling power for a <5 K experiment. A decoupling system suppresses vibrations from the cryocooler by three orders of magnitude down to a level of 10 nm peak amplitudes in the horizontal plane. Heat loads of about 40 W (at 45 K) and 1 W (at 4 K) are transferred from an experimental chamber, mounted on an optical table, to the cryocooler through a vacuum-insulated massive 120 kg inertial copper pendulum. The 1.4 m long pendulum allows installation of the cryocooler in a separate, acoustically isolated machine room. At the experimental chamber, we measured the residual vibrations using an interferometric setup. The positioning of the 4 K elements is reproduced to better than a few micrometer after a full thermal cycle to room temperature. Extreme high vacuum on the 10−15 mbar level is achieved. In collaboration with the Max-Planck-Institut für Kernphysik, such a setup is now in operation at the Physikalisch-Technische Bundesanstalt for a next-generation optical clock experiment using highly charged ions.