An important requirement of wastewater treatment plants (WWTPs) is compliance with the local regulations on effluent discharge, which are going to become more stringent in the future. The operation of WWTPs exhibits a trade-off between operational cost and effluent quality, which provides a scope for optimization. Process optimization is usually done by optimizing a model of the process. However, due to inevitable plant-model mismatch, the computed optimal solution is usually not optimal for the plant. This study represents the first attempt to handle plant-model mismatch via constraint adaptation (CA) for the real-time optimization of WWTPs. In this simulation study, the "plant" is a model adopted from the BSM1 benchmark, while a reduced-order "model" is used for making predictions and computing the optimal inputs. A first implementation uses steady-state measurements of the plant constraints to adjust the model in the optimization framework. A fast CA technique is also proposed, which adjusts the model using transient measurements. It is observed that, even in the presence of significant plant-model mismatch, the two proposed techniques are able to meet the active plant constraints. These techniques are found to reduce the pumping and aeration energy by 20%, as compared to that adopted in BSM1.