The light emission rate of a single quantum dot can be drastically enhanced by embedding it in a resonant semiconductor microcavity. This phenomenon is known as the Purcell effect, and the coupling strength between emitter and cavity can be quantified by the Purcell factor. The most natural way for probing the Purcell effect is a time-resolved measurement. However, this approach is not always the most convenient one, and alternative approaches based on a continuous-wave measurement are often more appropriate. Various signatures of the Purcell effect can indeed be observed using continuous-wave measurements (increase of the pump rate needed to saturate the quantum dot emission, enhancement of its emission rate at saturation, change of its radiation pattern), signatures which are encountered when a quantum dot is put on-resonance with the cavity mode. All these observations potentially allow one to estimate the Purcell factor. In this paper, we carry out these different types of measurements for a single quantum dot in a pillar microcavity and we compare their reliability. We include in the data analysis the presence of independent, non-resonant emitters in the microcavity environment, which are responsible for a part of the observed fluorescence.