Even though COVID-19 is no longer the primary focus of the global scientific community, its high mutation rate (nearly 30 substitutions per year) poses a threat of a potential comeback. Effective vaccines have been developed and administered to the population, ending the pandemic. Nonetheless, reinfection by newly emerging subvariants, particularly the latest JN.1 strain, remains common. The rapid mutation of this virus demands a fast response from the scientific community in case of an emergency. While the immune escape of earlier variants was extensively investigated, one still needs a comprehensive understanding of how specific mutations, especially in the newest subvariants, influence the antigenic escape of the pathogen. Here, we tested comprehensive in silico approaches to identify methods for fast and accurate prediction of antibody neutralization by various mutants. As a benchmark, we modeled the complexes of the murine antibody 2B04, which neutralizes infection by preventing the SARS-CoV-2 spike glycoprotein’s association with angiotensin-converting enzyme (ACE2). Complexes with the wild-type, B.1.1.7 Alpha, and B.1.427/429 Epsilon SARS-CoV-2 variants were used as positive controls, while complexes with the B.1.351 Beta, P.1 Gamma, B.1.617.2 Delta, B.1.617.1 Kappa, BA.1 Omicron, and the newest JN.1 Omicron variants were used as decoys. Three essentially different algorithms were employed: forced placement based on a template, followed by two steps of extended molecular dynamics simulations; protein–protein docking utilizing PIPER (an FFT-based method extended for use with pairwise interaction potentials); and the AlphaFold 3.0 model for complex structure prediction. Homology modeling was used to assess the 3D structure of the newly emerged JN.1 Omicron subvariant, whose crystallographic structure is not yet available in the Protein Database. After a careful comparison of these three approaches, we were able to identify the pros and cons of each method. Protein–protein docking yielded two false-positive results, while manual placement reinforced by molecular dynamics produced one false positive and one false negative. In contrast, AlphaFold resulted in only one doubtful result and a higher overall accuracy-to-time ratio. The reasons for inaccuracies and potential pitfalls of various approaches are carefully explained. In addition to a comparative analysis of methods, some mechanisms of immune escape are elucidated herein. This provides a critical foundation for improving the predictive accuracy of vaccine efficacy against new viral subvariants, introducing accurate methodologies, and pinpointing potential challenges.