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This paper describes an approach for the noninvasive microwave characterization of tumors in breast tissue. Tumors are modeled as lossy dielectric targets. Their complex natural resonances (CNR) can be extracted from the time-domain response and correlated with diagnostically useful properties. Finite-difference time-domain simulation is used to obtain the time-domain response from a tumor with a short electromagnetic pulse as an input. The normal breast tissue and tumor are modeled as dispersive media using the Debye model and CNRs are extracted using Prony's method. It is shown that the locations of the dominant CNRs are separated in the complex frequency plane as functions of the tumor dielectric properties. The technique has potential as a diagnostic tool to characterize breast lesions in conjunction with other imaging modalities such as ultrasound for detection.