There are well-known non-euclidean models that are created in euclidean geometry, for example the Beltrami-Klein model. This "nesting" proves the consistency of non-euclidean geometry (it is consistent if euclidean geometry is consistent).
I have heard that it is possible to build a model of Euclidean geometry inside non-Euclidean geometry, but I couldn't find any examples. Could you please provide some.