Swing options are widely used in electricity markets for the price and volume flexibility reasons they provide. Due to their multiple exercise property, the pricing of swing options requires sophisticated numerical methods. So far such methods have mostly been based on Monte-Carlo methods. We want to price swing options efficiently, leading to variational inequalities in the mathematical model which can also be interpreted as obstacle problems. Fine discretizations that are needed for such obstacle problems resolve in high dimensional problems and thus in long computing times. To reduce the dimensionality of such problems, we use the Reduced Basis Method (RBM). The objective of the RBM is to efficiently reduce discretized parametrized partial differential equations. Problems are considered where not only a single solution is needed but solutions for a range of different parameter configurations. In the context of variational inequalities, RBM have already been applied to the elliptic case. However, in the case of swing options - therefore time-dependent - we have to consider the class of parabolic variational inequalities. Recent work on American Options combines RBM with parabolic variational inequalities, but does not provide error estimators. In our work, error estimators could be achieved by combining RBM with a space-time formulation.