Geolocation of Internet hosts enables a new class of location-aware applications. Previous measurement-based approaches use reference hosts, called landmarks, with a well-known geographic location to provide the location estimation of a target host. This leads to a discrete space of answers, limiting the number of possible location estimates to the number of adopted landmarks. In contrast, we propose Constraint-Based Geolocation (CBG), which infers the geographic location of Internet hosts using multilateration with distance constraints to establish a continuous space of answers instead of a discrete one. However, to use multilateration in the Internet, the geographic distances from the landmarks to the target host have to be estimated based on delay measurements between these hosts. This is a challenging problem because the relationship between network delay and geographic distance in the Internet is perturbed by many factors, including queueing delays and the absence of great-circle paths between hosts. CBG accurately transforms delay measurements to geographic distance constraints, and then uses multilateration to infer the geolocation of the target host. Our experimental results show that CBG outperforms previous geolocation techniques. Moreover, in contrast to previous approaches, our method is able to assign a confidence region to each given location estimate. This allows a location-aware application to assess whether the location estimate is sufficiently accurate for its needs.