Absorbed power of nanoparticles during magnetic hyperthermia can be well determined from changes in the quality factor ($Q$ factor) of a resonator, in which the radiofrequency (RF) absorbent is placed. We present an order of magnitude improvement in the $Q$ factor measurement accuracy over conventional methods by studying the switch-on and off transient signals of the resonators. A nuclear magnetic resonance (NMR) console is ideally suited to acquire the transient signals and it also allows to employ the so-called pulse phase-cycling to remove transient artifacts. The improved determination of the absorbed power is demonstrated on various resonators in the 1-30 MHz range including standard solenoids and also a birdcage resonator. This leads to the possibility to detect minute amounts of ferrite nanoparticles which are embedded in the body and also the amount of the absorbed power. We demonstrate this capability on a phantom study, where the exact location of an embedded ferrite is clearly detected.