We describe a quantitative, high-precision, high-throughput method for measuring the mechanical properties of cells in suspension with a microfluidic device, and for relating cell mechanical responses to protein expression levels. Using a high-speed (750 fps) charge-coupled device camera, we measure the driving pressure Δp, maximum cell deformation εmax, and entry time tentry of cells in an array of microconstrictions. From these measurements, we estimate population averages of elastic modulus E and fluidity β (the power-law exponent of the cell deformation in response to a step change in pressure). We find that cell elasticity increases with increasing strain εmax according to E ∼ εmax, and with increasing pressure according to E ∼ Δp. Variable cell stress due to driving pressure fluctuations and variable cell strain due to cell size fluctuations therefore cause significant variability between measurements. To reduce measurement variability, we use a histogram matching method that selects and analyzes only those cells from different measurements that have experienced the same pressure and strain. With this method, we investigate the influence of measurement parameters on the resulting cell elastic modulus and fluidity. We find a small but significant softening of cells with increasing time after cell harvesting. Cells harvested from confluent cultures are softer compared to cells harvested from subconfluent cultures. Moreover, cell elastic modulus increases with decreasing concentration of the adhesion-reducing surfactant pluronic. Lastly, we simultaneously measure cell mechanics and fluorescence signals of cells that overexpress the GFP-tagged nuclear envelope protein lamin A. We find a dose-dependent increase in cell elastic modulus and decrease in cell fluidity with increasing lamin A levels. Together, our findings demonstrate that histogram matching of pressure, strain, and protein expression levels greatly reduces the variability between measurements and enables us to reproducibly detect small differences in cell mechanics.