Screen top aquarium style I presume. There's a few tricks of the trade here.
1. Mist twice daily. Mist the walls of the enclosure, not so much to get things soaked, but enough to leave a nice amount of droplets to evaporate.
2. Use a wet towel to cover 2/3-3/4 of the top. Wetter than damp, but not wet enough to actually drop down into the tank. Wet substrate is usually bad unless it's a substrate that handles moister well... which brings me to...
3. Switch substrates to something that holds moisture and humidity better. Eco-Earth, peat moss, cypress mulch, etc.
4. Without switching substrates entirely, you can of course use a similar concept to the "moist hide", and just get an open container of decent size, throw some wet sphagnum moss in it and nestle it in there somewhere.
5. Put in another, considerably larger water bowl. On the warm side somewhere. The heat will help the water constantly evaporate, raising the humidity levels a little bit.
6. DON'T USE HEAT BULBS OR CERAMIC HEAT EMITTERS. They may be cheap and awesome, but they dry the air out around them something fierce. Under tank heaters and, for custom enclosures, radiant heat panels are the best sources of heat in the sense that they don't produce light and don't dry the air near as much.
Hope at least some of that helps.