We study the statistical-mechanical properties of intertwined double-helical DNAs (DNA braids). In magnetic tweezers experiments we find that torsionally-stressed stretched braids supercoil via an abrupt buckling transition, which is associated with nucleation of a braid end loop, and that the buckled braid is characterized by proliferation of multiple domains. Differences between the mechanics of DNA braids and supercoiled single DNAs can be understood as an effect of increased bulkiness in the structure of the former. The experimental results are in accord with the predictions of a previously-described statistical-mechanical model.