An automated framework is presented for characterization and behavioral modeling of GaN MMIC varactors for tunable matching network applications. The behavioral approach is applied by vector-fitting the impedance response and automatically synthesizing an equivalent-circuit network. The methodology addresses tracking the supply-dependent optimum point of power-added efficiency (PAE) of an amplifier stage across different power levels. The behavioral modeling approach is compared to measurement-based characterization and physics-based approaches to derive an equivalent circuit. The proposed behavioral modeling framework is extensively validated with two fabricated varactor devices in a realized matching network to achieve maximum PAE for an amplifier over a range of output power.