Coumarin derivatives have proven beneficial biological activities, but the mechanism of their radical scavenging potency is not fully understood. In this study, the antiradical capacity of two newly synthesized 4,7-dihydroxycoumarin derivatives: (E)-3-(1-((3-hydroxy-4-methoxyphenyl)amino)-ethylidene)-2,4-dioxochroman-7-yl acetate (A-3OH) and (E)-3-(1-((4-hydroxy-3-methoxyphenyl)amino)ethylidene)-2,4-dioxochroman-7-yl acetate (A-4OH) towards HO• were examined by Electron Paramagnetic Resonance (EPR) Spectroscopy and Density Functional Theory (DFT). The compounds were fully characterized by the elemental microanalysis, IR, and NMR spectroscopies. The effect of pH on the acid–base equilibria is separately discussed and the predominant species at the physiological pH were determined. Several common mechanisms (Hydrogen Atom Transfer (HAT), Single-Electron Transfer followed by Proton Transfer (SET-PT), Sequential Proton Loss followed by Electron Transfer (SPLET), Radical Adduct Formation (RAF), and Intramolecular Hydrogen Atom Abstraction (iHAA)) of radical scavenging were investigated based on thermodynamic and kinetic parameters. EPR results indicated that both compounds significantly reduce the amount of present HO•. The results of the kinetic DFT study demonstrated that both compounds predominantly exhibit antiradical capacity through HAT and SPLET mechanisms. The estimated overall rate constants (koverall) proved that A-4OH shows better antioxidant capacity than A-3OH which is well-correlated with the results obtained by EPR measurement.