Vibrotactile rendering is one of the most popular means for improving the user interface of a mobile device, but the availability of related perceptual data that can aid vibrotactile effect design is not currently sufficient. The present paper reports data from a series of psychophysical studies designed to fill this gap. In Experiment I, we measured the absolute detection thresholds of sinusoidal vibrotactile stimuli transmitted to the hand through a mobile phone. Stimuli were generated by a mechanical shaker system that can produce vibrations over a broad frequency and amplitude range. The detection thresholds reported here are a new addition to the literature, and can serve as a baseline for vibrotactile stimulus design. In Experiment II, we estimated the perceived intensities of mobile device vibrations for various frequencies and amplitudes using the same shaker system. We also determined a form of parametric nonlinear function based on Stevens' power law and fit the function to the measured data. This psychophysical magnitude function, which maps vibration frequency and amplitude to a resulting perceived intensity, can be used to predict the perceived intensity of a mobile device vibration from its physical parameter values. In Experiment III, we measured another set of perceived intensities using two commercial miniature vibration actuators (vibration motor and voice-coil actuator) in place of the mechanical shaker. The purpose of this experiment was to evaluate the utility of the psychophysical magnitude function obtained in Experiment II, as vibrotactile stimuli produced by miniature actuators may have different physical characteristics, such as vibration direction and ground condition. Comparison of the results of Experiments II and III confirmed that the psychophysical magnitude function can reliably predict changing trends in the perceived intensity of mobile device vibration. We also discuss further research issues encountered during the investigation. The results presented in this paper may be instrumental in the design of effective vibrotactile actuators and perceptually-salient rendering algorithms for mobile devices.