We describe three recombinant engineered antibodies against three recombinant epitope tags, constructed with divalent binding arms to recognize divalent epitopes and so achieve high affinity and specificity. In two versions, an epitope is inserted in tandem into a protein of interest, and a homodimeric antibody is constructed by fusing a high-affinity epitope-binding domain to a human or mouse Fc domain. In a third, a heterodimeric antibody is constructed by fusing two different epitope-binding domains which target two different binding sites in GFP, to polarized Fc fragments. These antibody/epitope pairs have affinities in the low picomolar range and are useful tools for many antibody-based applications