Antioxidant polymers of the present invention comprise repeat units that include one or both of Structural Formulas (I) and (II): wherein: R is --H or a substituted or unsubstituted alkyl, acyl or aryl group; Ring A is substituted with at least one tert-butyl group or substituted or unsubstituted n-alkoxycarbonyl group; Ring B is substituted with at least one --H and at least one tert-butyl group or substituted or unsubstituted n-alkoxycarbonyl group; Rings A and B are each optionally substituted with one or more groups selected from the group consisting of --OH, --NH, --SH, a substituted or unsubstituted alkyl or aryl group, and a substituted or unsubstituted alkoxycarbonyl group; n is an integer equal to or greater than 2; and p is an integer equal to or greater than 0. The invention also includes methods of using and preparing these polymers.