Ultra-wideband (UWB) Microwave imaging (MWI) is a promising breast cancer detection technology which exploits the significant contrast in dielectric properties between normal breast tissue and tumor. Previously, data-independent methods, such as delay-and-sum (DAS) and space-time (ST) beamforming, have been used for microwave imaging. However, the low resolution and the poor interference suppression capability associated with the data-independent methods restrict their use in practice, especially when the noise is high and the backscattered signals are weak. In this paper, we develop two data-adaptive methods for microwave imaging, which are referred to as the robust weighted Capon beamforming (RWCB) method and the amplitude and phase estimation (APES) method. Due to their data-adaptive nature, these methods outperform their data-independent counterparts in terms of improved resolution and reduced sidelobe levels.