Patient studies and brain stimulation evidence suggest that language processing can be enhanced by altering the interhemispheric balance: namely, preferentially enhancing left-hemisphere activity while suppressing right-hemisphere activity. To our knowledge, no study has yet compared the effects of such bilateral brain stimulation to both logically necessary control conditions (separate left- and right-hemisphere stimulation). This study did so in a between-group sham-controlled design, applying transcranial direct current stimulation over Broca’s area and/or its homologue in 72 healthy participants. The effects were measured not only in a single-word-level task but also in a sentence-level task, rarely tested previously. We did not find either any significant overall effects of stimulation or greater stimulation effects in the bilateral compared to control groups. This null result, obtained in a large sample, contributes to the debate on whether tDCS can modulate language processing in healthy individuals.