In current credit risk models, default probabilities and recovery rates are often treated independently. However, when the structural connection between these quantities is neglected, the risk of large portfolio losses can be underestimated considerably. This problem becomes even more severe when calibration issues are taken into account. We calibrate different recovery rate models to Monte Carlo simulations of a structural reference model. The Merton model serves as our reference system with diffusion and jump diffusion as underlying processes. We find the most reliable and stable results for the structural recovery, which involves a functional relationship between recovery rates and default probabilities.