Fungal laccases are multicopper enzymes of industrial importance due to their high stability, multifunctionality, and oxidizing power. This paper reports computational protocols that quantify the relative stability (ΔΔG of folding) of mutants of high-redox-potential laccases (TvLIIIb and PM1L) with up to 11 simultaneously mutated sites with good correlation against experimental stability trends. Molecular dynamics simulations of the two laccases show that FoldX is very structure-sensitive, since all mutants and the wild type must share structural configuration to avoid artifacts of local sampling. However, using the average of 50 MD snapshots of the equilibrated trajectories restores correlation (r ~ 0.7-0.9, r(2) ~ 0.49-0.81) and provides a root-mean-square accuracy of ~1.2 kcal/mol for ΔΔG or 3.5 °C for T(50), suggesting that the time-average of the crystal structure is recovered. MD-averaged input also reduces the spread in ΔΔG, suggesting that local FoldX sampling overestimates free energy changes because of neglected protein relaxation. FoldX can be viewed as a simple "linear interaction energy" method using sampling of the wild type and mutant and a parametrized relative free energy function: Thus, we show in this work that a substantial "hysteresis" of ~1 kcal/mol applies to FoldX, and that an improved protocol that reverses calculations and uses the average obtained ΔΔG enhances correlation with the experimental data. As glycosylation is ignored in FoldX, its effect on ΔΔG must be additive to the amino acid mutations. Quantitative structure-property relationships of the FoldX energy components produced a substantially improved laccase stability predictor with errors of ~1 °C for T(50), vs 3-5 °C for a standard FoldX protocol. The developed model provides insight into the physical forces governing the high stability of fungal laccases, most notably the hydrophobic and van der Waals interactions in the folded state, which provide most of the predictive power.