Practical high-temperature superconductors must be textured to minimize the reduction of the critical current density J(gb) at misoriented grain boundaries. Partial substitution of Ca for Y in YBa2Cu3O7-delta has shown significant improvement in J(gb) but the mechanisms are still not well understood. Here we report atomic-scale, structural and analytical electron microscopy combined with transport measurements on 7 degrees [001]-tilt Y0.7Ca0.3Ba2Cu3O7-delta and YBa2Cu3O7-delta grain boundaries, where the dislocation cores are well separated. We show that the enhanced carrier density, higher J(gb) and weaker superconductivity depression at the Ca-doped boundary result from a strong, non-monotonic Ca segregation and structural rearrangements on a scale of similar to 1 nm near the dislocation cores. We propose a model of the formation of Ca2+ solute atmospheres in the strain and electric fields of the grain boundary and show that Ca doping expands the dislocation cores yet enhances J(gb) by improving the screening and local hole concentration.