Induction heating appliances use control algorithms to regulate the power delivered to the vessel in a wide range [50 W-3.5 kW]. Switching frequency is commonly used to control the delivered power, hence an accurate identification of the power-frequency function would be useful, especially in multiple-output power converters. However, this function exhibits a severe variability due to temperature or vessel-inductor geometrical alignment, what reduces the performance of the open-loop control strategies. A method is presented to estimate the power-frequency function in just half a period of the utility voltage. The method packs several switching frequencies in the short identification period. The load is modelled as an equivalent series resistance-inductance, where both parameters vary linearly with respect to the switching frequency. The method is able to safely estimate the function using only switching frequencies well above resonance, but crucially, it is able to extrapolate accurately the delivered power levels even close to resonance.