Color display calibration, in part, involves mapping input RGB values to corresponding output values in a standardized color space such as CIE XYZ. A linear model for RGB-to-XYZ mapping is based on a 3-by-3 linear transformation matrix T mapping data from (linearized) RGB to XYZ. Such a mapping is often determined by least squares regression on the difference between predicted and measured XYZ values. However, since displays are calibrated for viewing by human observers, it likely would be better to optimize relative to a perceptually uniform color space. Two new methods are proposed which optimize the total error relative to CIELAB or CIEDE2000. The first method uses weighted least squares with weights based on the rate of change of CIELAB coordinates as a function of change in XYZ. The second method uses Nedler-Mead nonlinear optimization to minimize directly in CIELAB or CIEDE200. Experiments based on calibrating 2 CRT monitors, 3 LCD monitors and 2 LCD projectors show significantly better results than the standard least squares calibration.