Silica-rich hydrous magmas are commonly stored in crustal reservoirs, but are also present at mantle depths in subduction contexts as a result of slab melting in the presence of considerable amounts of water and other vol-atile species. Magnetotelluric surveys frequently identify highly conductive zones at crustal or mantle depths possibly revealing the presence of such silica-rich melts and this can be used to trace the cycling of water in sub-duction zones and its relationship with arc-magmatism. The achievement of such a purpose is impeded by poor knowledge of the electrical conductivity of both dry and hydrous silica-rich melts at pressure. To fill this gap, we performed in situ electrical conductivity measurements on a dacitic melt using a 4-wire set up to 1300 °C, 3.0 GPa and H 2 O content up to 12 wt.%. Melt conductivity is strongly correlated with its water content, and we reveal a complex effect of pressure being relatively small at low water contents and major at high water contents: with increasing water content, the activation volume ranges between 4 (dry) and 25 cm 3 /mol (H 2 O = 12 wt.%) and the activation energy decreases from 96 kJ (dry) to 62 kJ (12 wt.% H 2 O). By comparison with diffusivity data, so-dium appears to be the main charge carrier, even at high (12 wt.%) water content. A T–P–[H 2 O] model predicting the conductivity of dacitic melts shows that crustal and mantle wedge conductive bodies can be interpreted by the presence of silica-rich, hydrous, partially crystallized magma.