Real-time power measurements performed by cellular receivers are essential for power control, handoff and dynamic channel allocation. For best results, the measurement filter bandwidth must be sufficiently narrow to average out multipath fluctuations, yet sufficiently wide to follow shadow fading fluctuations. Our study considers two measurement methods and two filter types. We show, using standard models for the multipath and shadow fadings, that the dB measurement error tends to be Gauss-distributed and zero-mean. The performance metric then becomes the standard deviation (δ) of the dB error, which can be minimized by proper choice of the filter bandwidth. We find that δ can be kept to values of 3dB or lower over a wide range of mobile velocities and shadow fading characteristics. Also, we discuss the potential gains in measurements accuracy associated with diversity reception and broadband channels.