Naringenin, a citrus-derived flavanone, was investigated using computational methods to characterize its predicted binding to cyclooxygenase-2 (COX-2), a target associated with inflammatory signaling and cancer-related biology, and to compare its interactions with COX-1. Molecular docking using AutoDock Vina yielded a predicted affinity of −9.47 kcal/mol for naringenin against human COX-2 (PDB ID: 5KIR), whereas the reference inhibitor rofecoxib showed a more favorable score of −10.15 kcal/mol under the same docking conditions. Redocking across three independent seeded runs reproduced the crystallographic rofecoxib pose, with a mean heavy-atom RMSD of 0.92 ± 0.001 Å (mean ± SD), supporting the ability of the selected protocol to reproduce the reference ligand pose. Docking to human COX-1 (PDB ID: 6Y3C) yielded less favorable scores; relative to COX-1, the COX-2 score was more favorable by 1.31 kcal/mol for naringenin and 2.82 kcal/mol for rofecoxib. Twenty-nanosecond explicit-solvent molecular dynamics simulations in GROMACS, using the AMBER99SB-ILDN protein force field and explicitly described ligand parameters, yielded mean backbone RMSDs of 0.128 and 0.191 nm for the naringenin–COX-2 and naringenin–COX-1 complexes, respectively. Ligand RMSD, ligand–binding-site minimum-distance analysis, and trajectory inspection suggested intra-pocket reorientation without observed dissociation during the simulated interval. MM-GBSA calculations yielded more favorable approximate binding-energy estimates for COX-2 than for COX-1 (−23.51 versus −20.16 kcal/mol), although these estimates should not be interpreted as experimentally determined free energies. In silico ADME profiling using SwissADME predicted high gastrointestinal absorption, no violations of the Lipinski, Ghose, Veber, Egan, and Muegge drug-likeness rules, and no PAINS or Brenk alerts. Overall, the computational results suggested a more favorable predicted interaction of naringenin with COX-2 than with COX-1 under the modeled conditions. Experimental enzyme-inhibition assays against both isoforms are required to determine whether this predicted preference corresponds to biochemical selectivity.