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Experimental airborne synthetic aperture radar (SAR) systems achieve spatial resolutions of approximately 10 cm, whereas the new spaceborne very high spatial resolution (VHR) SAR sensors onboard the TerraSAR-X and COSMO-SkyMed satellites achieve spatial resolutions down to 1 m. In VHR SAR data, features from individual urban structures (i.e., buildings) can be identified by their characteristic settings in urban settlement patterns. In this paper, we present a novel concept for the height estimation of generic man-made structures from single detected SAR data. The proposed approach is based on the definition of a hypothesis on the height of the building and on the simulation of a SAR image for testing that hypothesis. A matching procedure is applied between the estimated and the actual SAR image in order to test the height hypothesis. The process is iterated for different height assumptions until the matching function is optimized, and thus, the building height is estimated. The efficiency of the proposed method is demonstrated on a set of 40 flat- and gable-roof buildings using two submeter VHR airborne and two 1-m resolution TerraSAR-X SAR scenes all acquired from the same residential area in Dorsten, Germany. The results show that, in the absence of string disturbing effects, the method is able to estimate the height of flat- and gable-roof buildings in the submeter data to the order of a meter, while the accuracy for the meter resolution spaceborne data is lower but still sufficient to estimate the number of floors of a building.