Nanosecond laser-induced breakdown spectroscopy (ns-LIBS) is employed for quantitative local fuel-air (F/A) ratio (i.e., ratio of actual fuel-to-oxidizer mass over ratio of fuel-to-oxidizer mass at stoichiometry, measurements in well-characterized methane-air flames at pressures of 1-11 bar). We selected nitrogen and hydrogen atomic-emission lines at 568 nm and 656 nm, respectively, to establish a correlation between the line intensities and the F/A ratio. We have investigated the effects of laser-pulse energy, camera gate delay, and pressure on the sensitivity, stability, and precision of the quantitative ns-LIBS F/A ratio measurements. We determined the optimal laser energy and camera gate delay for each pressure condition and found that measurement stability and precision are degraded with an increase in pressure. We have identified primary limitations of the F/A ratio measurement employing ns-LIBS at elevated pressures as instabilities caused by the higher density laser-induced plasma and the presence of the higher level of soot. Potential improvements are suggested.