The design of low-temperature tunnel current converters and the design of a low-temperature damping stage for a scanning tunneling microscope (STM) are presented. The current amplifiers are able to measure very low tunnel current (down to 0.25 pA), while preserving a sufficient bandwidth for topographic and spectroscopic measurements and with very low noise characteristics (down to 3 fA Hz−1/2). The design of a compact low-temperature magnetic damping stage with a resonance frequency of about 7 Hz, protecting the microscope mechanics against mechanical vibrations of the cryostat is also described. The damped stage with the microscope mechanics is in contact with the cryostat during cooling, while during the STM measurements, it is mechanically isolated.