The results of two-dimensional micromagnetic modeling of magnetization patterns in Permalloy ellipses under the influence of rotating constant-amplitude magnetic fields are discussed. Ellipses of two different lateral sizes have been studied, 0.5m x 1.5m and 1m x 3m. The amplitude of the rotating magnetic field was varied between simulations with the condition that it must be large enough to saturate or nearly saturate the ellipse with the field applied along the long axis of the ellipse. For the smaller ellipse size it is found that the magnetization pattern forms an S state and the direction of the net magnetization lags behind the direction of the applied field. At a critical angle of the rotating magnetic field the direction of the magnetization switches by a large angle to a new S state. Both the critical angle and the angle interval of the switch depend on field amplitude. For this new state, it is instead the applied field direction that lags behind the magnetization direction. The transient magnetization patterns correspond to multi-domain patterns including two vortices, but this state never exists for the equilibrated magnetization patterns. The behavior of the larger ellipse in rotating field is different. With the field applied along the long-axis of the ellipse, the magnetization of the ellipse is nearly saturated with a vortex close to each apex of the ellipse. As the field is rotated, this magnetization pattern remains and the net-magnetization direction lags behind the direction of the field until for a certain angle of the applied field an equilibrium multi-domain state is created. Comparisons are made with corresponding experimental results obtained by performing in-field magnetic force microscopy on Permalloy ellipses.