Catalyzes the methylation of the para-4-hydroxyl of both eugenol and (iso)eugenol to methyleugenol and isomethyleugenol, respectively. The resulting products are part of a complex mixture of low-molecular-weight volatile compounds emitted by the flowers to attract pollinators. S-adenosyl-L-methionine + trans-isoeugenol = H(+) + S-adenosyl-L-homocysteine + trans-isomethyleugenol Homodimer. Expressed in petals, style and stamens, but not in stigma, sepals, leaves or stem tissues. Expressed during flower development with a peak just before anthesis. (iso)eugenol O-methyltransferase (IEMT) not only has distinct substrate specificity from Caffeic acid 3-O-methyltransferases (COMT), a highly homologous enzyme, but it also methylates the hydroxyl group at the para position rather than at the meta position as COMT does. Belongs to the class I-like SAM-binding methyltransferase superfamily. Cation-independent O-methyltransferase family. COMT subfamily.