Eutectic melting curves in the system MgO–SiO2 have been experimentally determined at lower mantle pressures using laser-heated diamond anvil cell (LH-DAC) techniques. We investigated eutectic melting of bridgmanite plus periclase in the MgO–MgSiO3 binary, and melting of bridgmanite plus stishovite in the MgSiO3–SiO2 binary, as analogues for natural peridotite and basalt, respectively. The melting curve of model basalt occurs at lower temperatures, has a shallower dT/dP slope and slightly less curvature than the model peridotitic melting curve. Overall, melting temperatures detected in this study are in good agreement with previous experiments and ab initio simulations at ∼25 GPa (Liebske and Frost, 2012; de Koker et al., 2013). However, at higher pressures the measured eutectic melting curves are systematically lower in temperature than curves extrapolated on the basis of thermodynamic modelling of low-pressure experimental data, and those calculated from atomistic simulations. We find that our data are inconsistent with previously computed melting temperatures and melt thermodynamic properties of the SiO2 endmember, and indicate a maximum in short-range ordering in MgO–SiO2 melts close to Mg2SiO4 composition. The curvature of the model peridotite eutectic relative to an MgSiO3 melt adiabat indicates that crystallization in a global magma ocean would begin at ∼100 GPa rather than at the bottom of the mantle, allowing for an early basal melt layer. The model peridotite melting curve lies ∼500K above the mantle geotherm at the core–mantle boundary, indicating that it will not be molten unless the addition of other components reduces the solidus sufficiently. The model basalt melting curve intersects the geotherm at the base of the mantle, and partial melting of subducted oceanic crust is expected.