DNA barcodes are short, unique ssDNA primers that “mark” individual biomolecules. To gain better understanding of biophysical parameters constraining primer–dimer formation between primers that incorporate barcode sequences, we have developed a capillary electrophoresis method that utilizes drag-tag-DNA conjugates to quantify dimerization risk between primer-barcode pairs. Results obtained with this unique free-solution conjugate electrophoresis approach are useful as quantitatively precise input data to parameterize computation models of dimerization risk. A set of fluorescently labeled, model primer-barcode conjugates were designed with complementary regions of differing lengths to quantify heterodimerization as a function of temperature. Primer–dimer cases comprised two 30-mer primers, one of which was covalently conjugated to a lab-made, chemically synthesized poly-N-methoxyethylglycine drag-tag, which reduced electrophoretic mobility of ssDNA to distinguish it from ds primer–dimers. The drag-tags also provided a shift in mobility for the dsDNA species, which allowed us to quantitate primer–dimer formation. In the experimental studies, pairs of oligonucleotide primer barcodes with fully or partially complementary sequences were annealed, and then separated by free-solution conjugate CE at different temperatures, to assess effects on primer–dimer formation. When less than 30 out of 30 base-pairs were bonded, dimerization was inversely correlated to temperature. Dimerization occurred when more than 15 consecutive base-pairs formed, yet non-consecutive base-pairs did not create stable dimers even when 20 out of 30 possible base-pairs bonded. The use of free-solution electrophoresis in combination with a peptoid drag-tag and different fluorophores enabled precise separation of short DNA fragments to establish a new mobility shift assay for detection of primer–dimer formation.