The present invention relates to a process for making the esters of 2,5-furandicarboxylic acid, and particularly the dimethyl, diethyl or dipropyl esters of FDCA for use as monomers in the production of polyesters and other types of polymers with biobased content, comprising: reacting an aqueous feed comprising glucaric acid with a high boiling first alcohol in the presence of an acid catalyst and with removing water during the reaction, to form a first product mixture comprising a first ester of FDCA and the high boiling first alcohol; removing unreacted high boiling first alcohol from the first product mixture; combining the first ester of FDCA and the high boiling first alcohol with a lower boiling second alcohol selected from the group consisting of methanol, ethanol, isopropanol and n-propanol; transesterifying the first ester with the lower boiling second alcohol to form a second product mixture comprising a second ester of FDCA with the lower boiling second alcohol; and recovering the second ester of FDCA with the lower boiling second alcohol.