Current standardized procedures for measurements of the Specific absorption rate (SAR) of mobile phones and radio base station antennas include a volumetric scan of the electric field strength induced in a head or body phantom. Assessment of multi-band and whole-body SAR requires repeated volumetric scanning over a large part of the phantom and is time-consuming. In order to reduce the total evaluation time, different methods have been proposed to estimate the SAR from measurement data based on sparse volumetric scanning and surface scanning. These methods rely on data fitting with underlying assumptions about the spatial distribution of the fields. In order not to be biased by previous or current antenna design, and to be able to use currently available assessment systems, a model-independent dual-plane-scan method is investigated based on amplitude measurements of the electric field components. The amplitude of the electric field components are measured in two planes close to the phantom surface, and the phase is recovered using an iterative process. The plane wave spectrum of the resulting complex electric field components is then used to propagate the field into the phantom. The measurement time is typically reduced by a factor 5 and in some cases even more. Furthermore, the plane wave spectrum is utilized for fast calculation of the mass-averaged local SAR values. A numerical tolerance study, using single and multi- peak fields with relevant errors superposed, is performed to demonstrate the robustness of the method. The resulting errors in the estimated SAR values are below 1% for realistic positioning errors and signal to noise ratio. Comparisons with measurements in a flat phantom are also made. Moreover, the underlying algorithm can be applied to curved surfaces.