Guanine-Uracil (GU) mismatches are crucial to the stability of the RNA double helix and need to be considered in RNA folding algorithms for numerous biotechnological applications. Yet despite its importance, many aspects of GU base pairs are still poorly understood. There is also a lack of parametrization which prevents it to be considered in mesoscopic models. Here, we adapted the mesoscopic Peyrard-Bishop model to deal with context-dependent hydrogen bonds of GU mismatches and calculated the model parameters related to hydrogen bonding and base stacking from available experimental melting temperatures. The context-dependence causes a proliferation of parameters which made the problem computationally very demanding. We were able to overcome this problem by systematically regrouping the parameters during the minimization procedure. Our results not only provide the much needed parametrization but also answer several questions about the general properties of GU base pairs, as they can be associated straightforwardly to hydrogen bonding and base stacking. In particular, we found a very small Morse potential for tandem 5'-GU-3', which confirms a single hydrogen bond for this configuration, answering a long-standing question over conflicting experimental findings. Terminal GU base pairs are known to increase the duplex stability, but it is not clear why. Our results suggest that the increased terminal stability is mostly due to stronger hydrogen bonding.