In recent years there has been a number of proposals of thermal devices operating in the near-field regime that make use of phase-transition materials. Here, we present a theoretical study of near-field thermal diodes and transistors that combine superconducting materials with normal (non-superconducting) metals. To be precise, we show that a system formed by two parallel plates made of Nb and Au can exhibit unprecedented rectification ratios very close to unity at temperatures around Nb superconducting critical temperature and for a wide range of gap size values within the near-field regime. Moreover, we also show that a superconducting Nb layer placed between Au plates can operate as a near-field thermal transistor where the amplification factor can be greatly tuned by varying different parameters such as the temperature and thickness of the Nb layer or the distance between the Nb layer and the Au plates. Overall, our work shows the potential of the use of superconductors for the realization of near-field thermal devices.