The accuracy of the positioning systems such as GPS, GLONASS or Galileo is heavily affected by the presence of the ionosphere. Ionosphere-free dual-frequency algorithms used for positioning applications remove most of the ionospheric error but do not take into account its higher-order terms. In addition, the raypaths and total electron content (TEC) are assumed to be the same for both frequencies. This leads to centimeter-level range errors that can cause millimeter-level errors in positioning. In this paper an accurate estimation of the higher-order ionospheric errors based on a realistic 3-D electron density model is presented. A numerical homing-in ray-tracing algorithm is implemented to rigorously calculate satellite to receiver ray trajectories. The numerical simulations performed showed that higher-order ionospheric residual range errors may reach several centimeters (up to 5 cm) at low and middle latitudes; however, at high latitudes they hardly exceed several millimeters (up to 1 cm).