For Compass and Galileo systems which are currently in their stage of construction, it is difficult to obtain precise on-board clock short-term stability for common users. In this paper, a simple estimation method based on smoothed broadcast ephemerides is proposed, which only needs observation from one single receiver. The principle of this method is discussed, followed by performance evaluation using GPS data. We conclude that the relative error of short-term stability estimated with this method is less than 10% for average time of 1~800 seconds. Short-term stability estimation of all the current 14 Compass on-board clocks are presented, with the result of approximately 6×10-12 at average time of 1s and 2×10-13 at 1000s.