Depth map upsampling is an approach to increase the spatial resolution of depth maps obtained from a depth camera. Depth map quality is closely related to 3D perception of stereoscopic image, multi-view image and holography. In general, the performance of upsampled depth map is evaluated by PSNR (Peak Signal to Noise Ratio). On the other hand, time-consuming 3D subjective tests requiring human subjects are carried out for examining the 3D perception as well as visual fatigue for 3D contents. Therefore, if an objective metric is closely correlated with a subjective test, the latter can be replaced by the objective metric. For this, this paper proposes a best metric by investigating the relationship between diverse objective metrics and 3D subjective tests. Diverse reference and no-reference metrics are adopted to evaluate the performance of upsampled depth maps. The subjective test is performed based on DSCQS test. From the utilization and analysis of three kinds of correlations, we validated that SSIM and Edge-PSNR can replace the subjective test.