The crucial question of whether the superconducting phase found in the spin ladder compound Sr14-xCaxCu24O41 is due to the natural pair forming mechanism predicted for isolated ladders is still open. A recent experimental breakthrough enables us to perform calorimetric measurements under hydrostatic pressure in a diamond anvil cell. We report here measurements on the compound Sr2.5Ca11.5Cu24O41 which show that the superconductivity is a bulk property and that antiferromagnetic order and superconductivity coexist over a wide pressure range. At the pressure where the sample becomes superconducting, the variation of the Neel temperature is continuous, However at high pressure there is a sharp increase of T-N, and T-N and T-C become comparable. The possible nature of the superconducting phase is discussed in the light of these results and previous measurements of the upper critical field.