I always suggest keeping tortoise pens as open as possible. In general, tortoises require better airflow than other reptiles; At least in the sense that they do not do well in an aquarium-type enclosure. The walls of glass terrariums are too high and block off airflow, making it easy for the ammonia from their urine to build up, and heat to build up from the stagnant air. So providing some fresh air not only helps to clear the ammonia, but makes sure that it doesn't overheat.
That doesn't mean it's not possible to keep a tortoise in an aquarium, it just takes some work. I've seen some people use computer fans to regulate the airflow and temperature, but I think most people decide that for the amount of work it would take, it's better to build a custom habitat with lower walls. It's also just more important to have floor space than wall height, since it's not like the tortoises are likely to climb out.
If you're using the exo-terra coconut fiber bedding, that actually holds moisture really well. The sphagnum moss does too. You don't want the soil to be soggy, but if you mist it with a spray bottle enough to keep it moist, that should keep the enclosure humid even with a screen top. Simply having a dish of water also helps add to the humidity too.
Plants are also really good at helping to keep enclosures humid. if you have the space you could add some plants. Even some edible plants.
I haven't needed them, but other options would be getting an automatic mister or reptile fogger. It's always a good idea to keep track of the humidity still. Don't assume that because it's automatic, that it's correct. Always keep a thermometer and a humidity gauge in your enclosures.
It's also important to remember that too much humidity can be bad as well. It can cause respiratory issues. You'll be shooting for a humidity of about 70%.