Non slip "rubber" mesh is good. Keep the little plastic boxes that Milling Cutters come in. You will find all sorts of plastic trays, and boxes around the home that can be modified / recycled into tool storage. Just remove all traces of their former use to prevent any corrosion.
In the drawers of a big Roller Cabinet I have used cardboard, folded to make deep ridged "slots to store spanners, so that Whit, A/F and metric do not intermingle. Surprisingly long lived, too!
As Neil says, MDF can be milled / bored to make storage for cutters, Taps, and Dies. (The Tap and Die Company do just this for their boxed sets) Sometimes these can be combined with a soft underlay. Seven day pill boxes may be handy for some small items.
Your ingenuity will find other ways.
Howard