Near-field communication comes to be an indispensable part of the future sixth generation (6G) communications at the arrival of the forth-coming deployment of extremely large-scale multiple-input-multiple-output (XL-MIMO) systems. Due to the huge array aperture and high-frequency bands, the electromagnetic radiation field is modeled by the spherical waves instead of the conventional planar waves, leading to severe weak sparsity to angular-domain near-field channel. Therefore, the channel estimation reminiscent of the conventional compression sensing (CS) approaches in the angular domain, judiciously utilized for low pilot overhead, may result in unprecedented challenges. To this end, this paper proposes a brand-new near-field channel estimation scheme by exploiting the naturally occurring useful side information. Specifically, we formulate the dual-band near-field communication model based on the fact that high-frequency systems are likely to be deployed with lower-frequency systems. Representative side information, i.e., the structural characteristic information derived by the sparsity ambiguity and the out-of-band spatial information stemming from the lower-frequency channel, is explored and tailored to materialize exceptional near-field channel estimation. Furthermore, in-depth theoretical analyses are developed to guarantee the minimum estimation error, based on which a suite of algorithms leveraging the elaborating side information are proposed. Numerical simulations demonstrate that the designed algorithms provide more assured results than the off-the-shelf approaches in the context of the dual-band near-field communications in both on- and off-grid scenarios, where the angle of departures/arrivals are discretely or continuously distributed, respectively.