During the solar wind dynamic pressure enhancement, around 0200 UT on January 11, 1997, at the end of the January 6–11 magnetic cloud event, the magnetopause was pushed inside geosynchronous orbit. The LANL 1994–084 and GMS 4 geosynchronous satellites crossed the magnetopause and moved into the magnetosheath. Also, the Geotail satellite was in the magnetosheath while the Interball 1 satellite observed magnetopause crossings. This event provides an excellent opportunity to test and validate the prediction capabilities and accuracy of existing models of the magnetopause location for producing space weather forecasts. In this paper, we compare predictions of two models: the Petrinec and Russell  model and the Shue et al.  model. These two models correctly predict the magnetopause crossings on the dayside; however, there are some differences in the predictions along the flank. The Shue et al.  model correctly predicts the Geotail magnetopause crossings and partially predicts the Interball 1 crossings. The Petrinec and Russell  model correctly predicts the Interball 1 crossings and is partially consistent with the Geotail observations. We further found that some of the inaccuracy in Shue et al.'s predictions is due to the inappropriate linear extrapolation from the parameter range for average solar wind conditions to that for extreme conditions. To improve predictions under extreme solar wind conditions, we introduce a nonlinear dependence of the parameters on the solar wind conditions to represent the saturation effects of the solar wind dynamic pressure on the flaring of the magnetopause and saturation effects of the interplanetary magnetic field Bz on the subsolar standoff distance. These changes lead to a better agreement with the Interball 1 observations for this event.