We present a detailed study of the use of Fabry-Perot (FP) cavities for the spectroscopy of single InAs quantum dots (QDs). We derive optimal cavity characteristics and resolution limits and measure photoluminescence linewidths as low as 0.9 GHz. By embedding the QDs in a planar cavity, we obtain a sufficiently large signal to actively feed back on the length of the FP to lock to the emission of a single QD with a stability below 2% of the QD linewidth. An integration time of approximately two seconds is found to yield an optimum compromise between shot noise and cavity length fluctuations. (C) 2009 Optical Society of America