In this paper we report on measurements and simulations of superconducting tubes in the presence of inhomogeneous externally applied magnetic fields in a cryogenic environment. The shielding effect is studied for two different tube materials, Pb and Nb, employing Hall sensors in a tabletop experiment. The measured internal and external fields of the tubes agree with the theory of the Meissner-Ochsenfeld effect [1], field trapping of type 2 superconductors, phase transitions and tube geometries. The obtained measurements are compared to a finite element simulation. Next, the simulation model is applied to estimate the shielding effect in the vicinity of a cryogenic Penning trap experiment. The controlled suppression of external magnetic fields is important for future precision experiments in atomic and antimatter physics in cryogenic environments.