How can I prepare for a closed book comparative essay?

One technique that can be really helpful is to set up a table of key themes, which for history could be something like social, economic, religious or ideological factors, and then create a column for each of the things you are comparing whether that be political leaders, civilisations or events. Under these columns you can also include a few useful quotes or statistics. This can be really helpful when essay writing as you already have ideas organised thematically that you can easily turn into paragraphs to answer an essay question. Also if you start your revision by trying to fill in a table of this sort from the information you have off the top of your head, you can get an idea of the areas you might need to review or don't have as much information on.