Advanced location based services will in the following years increasingly require database technologies capable of tracking the positions of large amounts of continuously moving objects. Such positions are inherently imprecise. Previous work addressed separately indexing of the positions of moving objects and modeling the uncertainty about these positions. This paper addresses the problem of handling uncertainty when indexing the current and anticipated near-future positions of continuously moving objects. Two approaches for handling the uncertainty are explored. The first approach incorporates uncertainty information into the index structure. The second approach handles uncertainty by expanding the query region. The TPR-tree is used as an indexing method. Performance experiments show that both methods show similar query performance, but the index-based approach is more flexible when other factors are considered.