A great concern to have. For all studies I have used plastic bins with lids, but holes drilled in the lid for air (RH) circulation. In the case of open dish studies, we added a layer of cheese cloth over the open dish positioned in the floor of the bin. The dish was also taped to the floor of the bin to prevent spillage if the bin were tipped. (Have to use moisture resistant tape, such as certain kinds of duct tape). Would love to hear what others have done.