The estimation of protein model accuracy (EMA) or model quality assessment (QA) is important for protein structure prediction. An accurate EMA algorithm can guide the refinement of models or pick the best model or best parts of models from a pool of predicted tertiary structures. We developed two novel methods: MASS2 and LAW, for predicting residue‐specific or local qualities of individual models, which incorporate residual neural networks and graph neural networks, respectively. These two methods use similar features extracted from protein models but different architectures of neural networks to predict the local accuracies of single models. MASS2 and LAW participated in the QA category of CASP14, and according to our evaluations based on CASP14 official criteria, MASS2 and LAW are the best and second‐best methods based on the Z‐scores of ASE/100, AUC, and ULR‐1.F1. We also evaluated MASS2, LAW, and the residue‐specific predicted deviations (between model and native structure) generated by AlphaFold2 on CASP14 AlphaFold2 tertiary structure (TS) models. LAW achieved comparable or better performances compared to the predicted deviations generated by AlphaFold2 on AlphaFold2 TS models, even though LAW was not trained on any AlphaFold2 TS models. Specifically, LAW performed better on AUC and ULR scores, and AlphaFold2 performed better on ASE scores. This means that AlphaFold2 is better at predicting deviations, but LAW is better at classifying accurate and inaccurate residues and detecting unreliable local regions. MASS2 and LAW can be freely accessed from http://dna.cs.miami.edu/MASS2-CASP14/ and http://dna.cs.miami.edu/LAW-CASP14/, respectively.