Image sharpening is a post-processing technique employed for the artificial enhancement of the perceived sharpness by shortening the transitions between luminance levels or increasing the contrast on the edges. The greatest challenge in this area is to determine the level of perceived sharpness which is optimal for human observers. This task is complex because the enhancement is gained only until the certain threshold. After reaching it, the quality of the resulting image drops due to the presence of annoying artifacts. Despite the effort dedicated to the automatic sharpness estimation, none of the existing metrics is designed for localization of this threshold. Nevertheless, it is a very important step towards the automatic image sharpening. In this work, possible usage of full-reference image quality metrics for finding the optimal amount of sharpening is proposed and investigated. The intentionally over-sharpened "anchor image" was included to the calculation as the "anti-reference" and the final metric score was computed from the differences between reference, processed, and anchor versions of the scene. Quality scores obtained from the subjective experiment were used to determine the optimal combination of partial metric values. Five popular fidelity metrics - SSIM, MS-SSIM, IW-SSIM, VIF, and FSIM - were tested. The performance of the proposed approach was then verified in the subjective experiment.