EWS save contact or task email attachment to file

I'm able to read an email and get its item attachments (not file attachments) and want to save them to a file.  I'm trying to get the MimeContent for tasks and contacts attached to an email.  But, when I do, I get the following error:

MIME conversion is not supported for this item type

itemAttachment = attachment as ItemAttachment;
itemAttachment.Load(new PropertySet(ItemSchema.MimeContent));

I can recast the itemAttachment to a EWS Task or Contact object, and everything seems to be there.  How can I programatically create an EML file out of attached Tasks or Contacts?  The mimeContent approach seems to work for everything else....