When I want to loose cellulite/fat from my lower body spinning and/or running do the trick. I dont' see why a ellipital can't give you results. The main thing for me is at least 20 min of hiit followed by steady state for 40. I usually will do a 5 min power walk then do different sprint/run/jog intervals for 20 min followed by steady state jog/power walk. I also do a similar routine with the spin bike. I'm also 46 so I have to work harder to keep slim.
I found this article and if read toward the bottom of the article it address women's fat storage. I found this several years ago and incorporated the cardio suggestion to get rid of cellulite.
http://www.simplyshredded.com/the-ultimate-female-training-guide.html