In this paper an objective metric to measure the perceptual quality of watermarked 3D meshes is presented. The metric, which is based on a black-box approach, relies on the measurement of the roughness of 3D meshes before and after the insertion of the watermark. To calibrate the metric and to validate it, a set of psychovisual experiments has been carried out. Due to the lack of prior work in this field, a new methodology for the subjective evaluation of the quality of watermarked 3D objects is introduced. The validity of the proposed metric has been tested against a number of different 3D watermarking algorithms, showing an excellent match with the subjective evaluation of the quality stemming from the pshycovisual experiments.