Here is a list of some of the things you can do after you defeat the elite four in emerald version.

 

1) Go to the fossil maniac's house go through the tunnel and get the other fossil.

 

2) Go to battle fronteir

 

3) choose a color red to catch latias blue to catch latios.

 

4) go to the new area in the safari zone filled with johto pokemon.

 

5) CATCH EM ALL