O-methyltransferase that catalyzes the 2 O-methylation steps in the ubiquinone biosynthetic pathway. a 3-demethylubiquinol + S-adenosyl-L-methionine = a ubiquinol + H(+) + S-adenosyl-L-homocysteine a 3-(all-trans-polyprenyl)benzene-1,2-diol + S-adenosyl-L-methionine = a 2-methoxy-6-(all-trans-polyprenyl)phenol + H(+) + S-adenosyl-L-homocysteine Cofactor biosynthesis; ubiquinone biosynthesis. Belongs to the methyltransferase superfamily. UbiG/COQ3 family.