Chemo-enzymatic synthesis and screening of a library of renewable saturated and unsaturated bis- and trisphenols deriving from p-hydroxycinnamic acids (i.e., p-coumaric acid, ferulic acid, and sinapic acid) and biobased diols/triol (i.e., isosorbide, 1,4-butanediol, glycerol) showed that these compounds were potent antioxidants/antiradicals. To optimize their antiradical activities, we assessed the structure–activity relationships (SAR) of these phenolics focusing on the internal diol/triol linker, the degree of methoxylation on the aromatic rings, and the CC double bond of the α,β-unsaturated esters. We found that methoxylation degree and the unsaturation were critical for antiradical activity while the nature of the diol had a small impact. Indeed, SAR revealed that, for saturated compounds, the higher the methoxylation degree, the higher the antiradical activity; on the other hand, unexpectedly, the presence of the unsaturation had a negative impact on the activity. The antiradical activities of these bis- and trisphenols were then compared to that of Irganox 1010, a widely used antioxidant additive in polypropylene. The optimized compounds, i.e. those deriving from sinapic acid and with saturated esters, proved as effective while being 100% biobased and obtained through a more sustainable synthetic pathway. Thermal analyses (TGA) demonstrated that these bis- and trisphenols exhibit high thermal stability and that their T d5% can be easily tailored by playing with the structure of the bisphenol core. p-Hydroxycinnamic acids-based bis- and trisphenols are thus promising easily accessible, eco-friendly, and biocompatible antiradical additives for a sustainable approach to the stabilization of polymers in packaging and other applications.