The narrow bandwidth (BW) associated to small antennas featured by a high quality factor (Q) can be enhanced by the addition of a matching network. However, the impedance matching is a difficult and time-consuming process since it depends on the ability of the designer for selecting that suitable matching architecture that achieves the best trade-off between BW, complexity and implementation. In this paper, a systematic method for broadening the BW of handset antennas is proposed. The method is focused on those antennas whose input impedance near the first resonance can be modeled as an RLC series circuit. In order to develop the proposal, a mathematical analysis is carried out using a simple electrical model and the theoretical results are validated through simulations and by an experimental process. As a result, a systematic method for designing matching networks with a good balance between complexity and BW enhancement is obtained. Thus, the method described herein ensures one half of Fano's limit BW increment through a simple and methodic matching design.