Demand for niobium and tantalum is increasing exponentially as these are essential ingredients for the manufacture of, among others, capacitors in technological devices and ferroniobium. Mine tailings rich in such elements could constitute an important source of Nb and Ta in the future and so alleviate potential supply risks. This paper evaluates the possibility of recovering niobium and tantalum from the slags generated during the tin beneficiation process of mine tailings from the old Penouta mine, located in Spain. To do so, a simulation of the processes that would be required to beneficiate and refine both elements is carried out. After tin carbothermic reduction, the slags are sent to a hydrometallurgical process where at the end niobium oxide and tantalum oxide are obtained. Reagents, water and energy consumption, in addition to emissions, effluents and product yields are assessed. Certain factors were identified as critical, and recirculation was encouraged in the model to maximize production and minimize reagents use and wastes. With this simulation, considering 3000 production hours per year, the metal output from the tailings of the old mine could cover around 1% and 7.4% of the world annual Nb and Ta demand, respectively.