Some physically relevant non-linear models with solitons, which have target space S², are known to have submodels with infinitely many conservation laws defined by the eikonal equation. Here we calculate all the symmetries of these models and their submodels by the prolongation method. We find that for some models, like the Baby Skyrme model, the submodels have additional symmetries, whereas for others, like the Faddeev-Niemi model, they do not.