A collaborative virtual environment (CVE) allows remote users to access and modify shared data through networks, such as the Internet. However, when the users are connected via the Internet, the network latency problem may become significant and affect the performance of user interactions. Existing works to address the network latency problem mainly focus on developing motion prediction methods that appear statistically accurate for certain applications. However, it is often not known how reliable they are in a CVE. In this work, we study the sources of error introduced by a motion predictor and propose to address the errors by estimating the error bounds of each prediction made by the motion predictor. Without loss of generality, we discuss how we may estimate the upper and lower error bounds based on a particular motion predictor. Finally, we evaluate the effectiveness of our method extensively through a number of experiments and show the effectiveness of using the estimated error bound in an areabased visibility culling algorithm for DVE navigation.