AbstractA new generation of aeromagnetic data documents the post‐Caledonide rift evolution of the southwestern Barents Sea (SWBS) from the Norwegian mainland up to the continent‐ocean transition. We propose a geological and tectonic scenario of the SWBS in which the Caledonian nappes and thrust sheets, well‐constrained onshore, swing from a NE‐SW trend onshore Norway to NW‐SE/NNW‐SSE across the SWBS platform area. On the Finnmark and Bjarmeland platforms, the dominant inherited magnetic basement pattern may also reflect the regional and post‐Caledonian development of the late Paleozoic basins. Farther west, the pre‐breakup rift system is characterized by the Loppa and Stappen Highs, which are interpreted as a series of rigid continental blocks (ribbons) poorly thinned as compared to the adjacent grabens and sag basins. As part of the complex western rift system, the Bjørnøya Basin is interpreted as a propagating system of highly thinned crust, which aborted in late Mesozoic time. This thick Cretaceous sag basin is underlain by a deep‐seated high‐density body, interpreted as exhumed high‐grade metamorphic lower crust. The abortion of this propagating basin coincides with a migration and complete reorganization of the crustal extension toward a second necking zone defined at the level of the western volcanic sheared margin and proto‐breakup axis. The abortion of the Bjørnøya Basin may be partly explained by its trend oblique to the regional, inherited, structural grain, revealed by the new aeromagnetic compilation, and by the onset of further weakening later sustained by the onset of magmatism to the west.