Abstract: Superconducting devices subject to strong charging energy interactions and Coulomb blockade are one of the key elements for the development of nanoelectronics and constitute common building blocks of quantum computation platforms and topological superconducting setups. The study of their transport properties is nontrivial and some of their nonperturbative aspects are hard to capture with the most ordinary techniques. Here we present a matrix product state approach to simulate the real-time dynamics of these systems. We propose a study of their transport based on the analysis of the currents after quantum quenches connecting such devices with external leads. Our method is based on the combination of a Wilson chain construction for the leads and a mean-field BCS description for the superconducting scatterers. In particular, we employ a quasiparticle energy eigenbasis which greatly reduces their entanglement growth and we introduce an auxiliary degree of freedom to encode the device’s total charge. This approach allows us to treat nonperturbatively both their charging energy and coupling with external electrodes. We apply the technique to simulate the topological Kondo effect where multiple external leads are coupled to a Majorana Cooper-pair box.