Using the density matrix renormalization group (DMRG), we study the magnetization process of a quasi-1D version of the S = 1/2 Heisenberg model on the frustrated 2D Shastry-Sutherland lattice in a magnetic field. In particular, n-leg Shastry-Sutherland spin-tubes obtained by coupling n orthogonal dimer chains and applying periodic boundary conditions in the transverse direction are considered. In combination with analytical results obtained by PCUTs, for n = 2 we discuss the complete phase diagram in a magnetic field and identify a new type of Wigner crystal stabilized by the localization of bound states of triplons, leading to specific NMR signatures observable in experiments. For n = 4, in the case of ferromagnetic transverse couplings, preliminary QMC and DMRG results are in excellent agreement. In the fully antiferromagnetic case the results are compared to the ones of the full 2D system obtained by PCUTs and the possibility to gain new insights into this challenging 2D problem using the DMRG is discussed.