If you want to use "honor" as a concept (ie as a noun), there are two words you can use:
1.) "honor" in latin means "an honor", an award or distinction that someone earns, usually in battle or by reason of an office one holds.
2.) "honestas" refers to the concepts of virtue, strength, moral rectitude, generosity, etc., that we usually mean when we say that someone is "honorable".
So it depends on what you are trying to say. A brave, patient man who receives a knighthood from his king is receiving an "honor" but would probably be prouder of his "honestas".
The form of the word (specifically the ending) will change, too, depending on how it is used in a sentence. Can you be more specific about whether you are using it in a phrase, and what exactly you mean by it?
"Honoro" is a verb, as the other threads have explained, and means basically "to give someone honor", with the variations that have already been discussed. Most dictionaries would list it under its "infinitive" form, "honorare".
BTW, I am the "Latin translator" for the IAAH that you referred to. Sorry I have been unavailable for a while. Feel free to e-mail me if I can be of further help.
Fr Philip Bochanski