Honokiol is a natural bisphenol neolignan present in the bark of Magnolia officinalis, whose extracts have been employed in oriental medicine to treat several disorders, showing a variety of biological properties, including antitumor activity, potentially related to radical scavenging. Six bisphenol neolignans with structural motifs related to the natural bioactive honokiol were synthesized. Their chain-breaking antioxidant activity was evaluated in the presence of peroxyl (ROO•) and hydroperoxyl (HOO•) radicals by both experimental and computational methods. Depending on the number and position of the hydroxyl and alkyl groups present on the molecules, these derivatives are more or less effective than the reference natural compound. The rate constant of the reaction with ROO• radicals for compound 7 is two orders of magnitude greater than that of honokiol. Moreover, for compounds displaying quinonic oxidized forms, we demonstrate that the addition of 1,4 cyclohexadiene, able to generate HOO• radicals, restores their antioxidant activity, because of the reducing capability of the HOO• radicals. The antioxidant activity of the oxidized compounds in combination with 1,4-cyclohexadiene is, in some cases, greater than that found for the starting compounds towards the peroxyl radicals. This synergy can be applied to maximize the performances of these new bisphenol neolignans.