"President" is to "presidential" as "moderator" is to what?
Solution 1:
It's moderatorial, but consider the usage note.
Moderatorial (Chiefly Christian Church) adjective Of, relating to, or characteristic of a moderator or chairman. - ODO
Here are some usage examples drawn from the internet:
This is a moderatorial note that there appears to be somewhat of a 'personal' edge appearing in these discussions and that could easily lead to us locking this thread. - scruffyduck, fsdeveloper.com
Not very moderatorial of me, I admit...but then a fella's gotta let his beard down sometime, right? - Chris Fitzgerals, talkbass.com
There's also the term moderatorly, but it doesn't appear in any of the dictionaries supported by OneLook. It also doesn't show up in Ngram's database. Here are some usage examples:
Moderatorly admonition: don't just post a link - CraigD, scienceforums.com
And if you think you have it tough, consider me, as I get emails about everything and some double when it pertains posts I made: I will get the moderation PM and email and I will get an email because I am the moderator. I get emails about everything I moderatorly do on the forums. - Ageless, boinc.berkeley.edu
Solution 2:
It's not a logical pair, but neutral or its synonym impartial fit nicely in your sentence.
http://www.oxforddictionaries.com/de/definition/englisch/neutral
Presidential is what you expect from a president, but from the moderator you expect him/her not to take sides.
Solution 3:
Why not "moderate"? (I mean the adjective, not the verb.) It doesn't precisely fit the analogy, in the sense that "moderate" does not mean, "like a moderator". On the other hand, it completes the sentence in a very satisfying manner.
Solution 4:
Lawrence's suggestion of moderatorial answers the fundamental question, but I'd like to suggest a more general approach: be more specific about the moderator's behavior.
I can gather that moderatorial means like a moderator, but what does that really tell me? What does like a moderator actually mean?
Was the moderator favoring one candidate over the other? Were they jumping in and offering their own opinions? Were they dressed up like a dinosaur? Did they fail to control the crowd? Something else entirely?
In any case, there are more specific words for any of the above. Consider using them instead.
This might not be very satisfying for your original question, but maybe it'll help somebody in a similar situation in the future.
Solution 5:
The difficulty in this case is that the word "moderator" describes a person based on what they are doing, whereas the word "president" is used strictly as a role title. You can say "Elena moderated the debate" but you can't say "Elena presidented the country", or even "Elena presided the country".
For these words to be directly comparable, you'd have to be able to change the suffix, '-tor', to a suffix '-ent'. But the words 'moderatent' or 'moderatant' don't exist.
Therefore it is better to use a word that describes a skill, such as adept. In particular, while a moderator is expected to be moderate, impartial or fair, they are also expected to be clear, have insightful questions and keep the debate interesting. In this capacity they act to the debate as an engine regulator would to the combustion cycle: ensuring it is neither too fast nor too slow.