Available bandwidth (ABW) estimation in wireless networks is a critical issue for quality-of-service (QoS) provisioning. Nowadays, a network path often contains at least one wireless link e.g., mobile users having wireless connection to the Internet through laptop PCs or smartphones. Most of the existing tools for measuring ABW have been developed and evaluated in wired networks. Since the characteristics of wired links and wireless links differ in many respects, such as fluctuations in capacity and stability due to the shared and unreliable nature of the wireless links, ABW estimation tools also need to be evaluated for network paths containing at least one wireless link. In this paper, we have extended our previous work, New Enhanced Available Bandwidth Estimation Technique (NEXT) by introducing a parameter-independent curve-fitting technique to detect the ABW from a one-way queuing delay signature and conducted a real test over a radio interface in a 4G/LTE mobile communication network. For the experiments, a commercial 4G/LTE mobile network of a Japanese mobile operator was used. Extensive simulations over an IEEE 802.11 network were also performed. Simulation results as well as real-world experimental results demonstrate that it is feasible to achieve reliable estimates under certain circumstances. Our extended approach, which we call NEXT-FIT, has very good ABW estimation results under conditions of different packet sizes, dynamic wireless link rates, and channel noises.