The analysis and modelling of magnetic anomalies at the conjugate rifted continental margins of the southern Iberia Abyssal Plain (TAP) and Newfoundland Basin have revealed that the sources of magnetic anomalies are distinctly different across both each margin and between the two margins. Analyses of synthetic anomalies and gridded sea surface magnetic anomaly charts west of Iberia and east of Newfoundland were accomplished by the methods of Euler deconvolution, forward and inverse modelling of the power spectrum, reduction-to-the-pole, and forward and inverse indirect methods. In addition, three near-bottom magnetometer profiles were analysed by the same methods in addition to the application of componental magnetometry. The results have revealed that oceanic crust, transitional basement and thinned continental crust are defined by magnetic sources with different characteristics. Over oceanic crust, magnetic sources are present as lava-flow-like bodies whose depths coincide with the top of acoustic basement seen on MCS profiles. Top-basement source depths are consistent with those determined in two other regions of oceanic crust. In the southern IAP, oceanic crust, ~4 km thick with magnetizations up to +1.5 A/m, generated by organized seafloor spreading was first accreted -126 Ma at the position of a N-S oriented segmented basement peridotite ridge. To the west, seafloor spreading anomalies can be modelled at spreading rates of 10 mm/yr or more. Immediately to the east, in a zone -10-20 km in width, I identify seafloor spreading anomahes which can only be modelled assuming variable spreading rates. In the OCT, sources of magnetic anomalies are present at the top of basement and up to -6 km beneath. I interpret the uppermost source as serpentinized peridotite, and the lowermost source as intruded gabbroic bodies which were impeded, whilst rising upwards, by the lower density serpentinized peridotites. Intrusion was accompanied by tectonism and a gradual change in conditions from rifting to seafloor spreading as the North Atlantic rift propagated northwards in Early Cretaceous times. Within thinned continental crust, sources are poorly lineated, and distributed in depth. Scaling relationships of susceptibility are consistent with the sources of magnetic anomalies within continental crust. OCT-type intrusions may be present in the mantle beneath continental crust. At the conjugate Newfoundland margin, seafloor spreading anomalies can be modelled at rates of 8 and 10 mm/yr suggesting an onset age consistent with that of the IAP. In the OCT there, I propose that magnetic anomalies are sourced in near top-basement serpentinized peridotites. An absence of magmatic material and the differences in basement character (with the IAP) suggest that conjugate margin evolution may have been asymmetric.