Pimpinella anisum L., or anise, is a plant that, besides its nutritional value, has been used in traditional medical practices and described in many cultures in the Mediterranean region. A possible reason for anise’s therapeutic value is that it contains coumarins, which are known to have many biomedical and antioxidant properties. HPLC analysis in our laboratory of the anise extract shows the presence of the coumarin esculetin. We used a hydrodynamic voltammetry rotating ring–disk electrode (RRDE) method to measure the superoxide scavenging abilities of anise seeds and esculetin, which has marked scavenging activity. A related coumarin, 4-methyl-esculetin, also showed strong antioxidant activity as measured by RRDE. Moreover, this study includes the X-ray crystal structure of esculetin and 4-methyl-esculetin, which reveal the H-bond and the stacking intermolecular interactions of the two coumarins. Coordinates of esculetin crystal structure were used to perform a DFT study to arrive at the mechanism of superoxide scavenging. Besides performing a H(hydroxyl) abstraction in esculetin position 6 by superoxide, the scavenging also includes the presence of a second superoxide radical in a π–π approach. Both rings of esculetin were explored for this attack, but only the pyrone ring was effective. As a result, one product of esculetin scavenging is H2O2 formation, while the second superoxide remains π–π trapped within the pyrone ring to form an esculetin-η-O2 complex. Comparison with other coumarins shows that subtle structural differences in the coumarin framework can imply marked differences in scavenging. For instance, when the catechol moiety of esculetin (position 6,7) is shifted to position 7,8 in 4-methyl-7,8-dihydroxy coumarin, that coumarin shows a superoxide dismutase action, which, beside H2O2 formation, includes the formation and elimination of a molecule of O2. This is in contrast with the products formed through esculetin superoxide scavenging, where a second added superoxide remains trapped, and forms an esculetin-η-O2 complex.