I once received a beauty box and since these are always really strong, they are perfect to store some of your makeup! If you receive such boxes often, you could even decide to have separate boxes for lip products, foundations, eye products etc.
I hope this convinced you that your old boxes shouldn't be in the garbage (unless you have so many that they are all empty). I used to buy storage boxes, but they are often very expensive while re-using other boxes works out just fine! Do you already re-use your old boxes?