For multiprimary displays, color within the interior of the gamut can be reproduced with several different control values, a situation that is in contrast with the three primary scenario, where the control values are unique. For a given color, the selection of the control values, or color calibration, becomes a fundamental step for color rendition on multiprimary devices. Because spatially smooth variations in color are common in imagery and it is critical that despite device variations these be maintained as smooth variations in renditions, it is also desirable that the calibration strategy preserve smoothness of the device control values over color space. Based on this motivation, we propose a variational framework for color calibration of multiprimary displays that emphasizes smoothness by minimizing the squared norm of the gradient of the calibration function over the display gamut. We test our proposed methodology on a four primary system, and compare its performance with calibrations obtained from other standard methodologies. Results indicate that, compared with the alternatives, the proposed variational approach offers the smoothest variation in the control values over the entire color space and as a result also exhibits enhanced robustness in the presence of device variations.