Transcranial electrical stimulation (tES) is being investigated as an experimental and clinical interventional technique in human participants. While promising, important limitations have been identified, including weak effect sizes and high inter- and intra-individual variability of outcomes. Here, we compared two “inhibitory” tES-techniques with supposedly different mechanisms of action as to their effects on performance in a visuospatial attention task, and report on a direct replication attempt. In two experiments, 2 × 20 healthy participants underwent tES in three separate sessions testing different protocols (10 min stimulation each) with a montage targeting right parietal cortex (right parietal–left frontal, electrode-sizes: 3cm × 3cm–7 cm × 5 cm), while performing a perceptual line bisection (landmark) task. The tES-protocols were compared as to their ability to modulate pseudoneglect (thought to be under right hemispheric control). In experiment 1, sham-tES was compared to transcranial alternating current stimulation at alpha frequency (10 Hz; α-tACS) (expected to entrain “inhibitory” alpha oscillations) and to cathodal transcranial direct current stimulation (c-tDCS) (shown to suppress neuronal spiking activity). In experiment 2, we attempted to replicate the findings of experiment 1, and establish frequency-specificity by adding a 45 Hz-tACS condition to α-tACS and sham. In experiment 1, right parietal α-tACS led to the expected changes in spatial attention bias, namely a rightward shift in subjective midpoint estimation (relative to sham). However, this was not confirmed in experiment 2 and in the complete sample. Right parietal c-tDCS and 45 Hz-tACS had no effect. These results highlight the importance of replication studies, adequate statistical power and optimizing tES-interventions for establishing the robustness and reliability of electrical stimulation effects, and best practice.