They are dried and kept as is in an acid-free paper packet or a small archival box.  We do not slice anything, but we do press plants flat.

Andy

I revised specimens in a herbarium where specimens are kept in a "swedish" system (paper envelope inside a flat box of 2 or 3 normalised sizes) and one of the previous curators used to press fungi flat. While Otidea specimens were easily doable even in this state (many 19th century specimens also look like that), I was told that the less fleshy gilled fungi such as small Mycena, Entoloma etc. lost their value by this treatment. In some cases it became impossible to revise them. The gills merged into one indistinguishable mass and it was impossible to make a section from gills. (If I remember correctly, he first made an exsiccate and then put it again into humid air and gradually flattened it before drying it again.) But really large fungi like Sarcosphaera, Morchella (or Boletus) are often cut into several thick pieces in other herbaria here, not only to spare place, but to make sure they dry up fast and thouroughly. Personally, I think anything larger than 1 cm will break into pieces anyway within 50-100 yrs, if they're only in envelopes, packed in small bales.

Thanks for the answers. So apparently there's some variety with the processing methods. With the gills of small fungi merging into one, probably there has been an excessive amount of weight used during the pressing.