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In this paper we present a hybrid approach for the measurement of the complex dielectric permittivities of arbitrarily shaped homogeneous dielectric scatterers by using microwaves. The proposed method is organized in two stages: in the first one, the supports of the scatterers are retrieved by means of a new formulation of the linear sampling method, which is based on the no sampling approach; in the second one, the complex permittivities of the targets are estimated by means of a quantitative method, which searches the solution within the constraints provided by the previous step. In such a way, the efficiency of the new version of the linear sampling method is combined with the accuracy of quantitative procedures. The proposed methodology is assessed against noisy synthetic data, by using the ant colony optimization algorithm as a tool to estimate the dielectric parameters of the inspected targets.