It does seem unusual for the results to be announced during the banquet, but since that is the way it is done at your school, you are wise to plan ahead for the different outcomes.
If he wins, you teach him to accept the honor with gratitude and humility and help him to realize that the margin of winning may have just been tipped by a single vote. You help him understand and remain aware of the new responsibility with which his fellow students have entrusted him. You support him in his new leadership role and encourage him to give his duties and responsibilities the proper time and attention they deserve.
If he does not win, you put your arms around him, hug him tightly, and tell him how proud you are of him for being in the honor society, for the great young man he is, for just being him. You acknowledge his disappointment and whatever feelings he has in the moment and support him as he deals with the loss. After he has had a little time to process the feelings, you help him understand that this is just one of MANY opportunities he will have to be a leader throughout his academic, personal, and professional life. You remind him that good leaders continue to persevere, despite setbacks, and move through the losses while looking ahead to new opportunities to serve.
Hope the outcome is a positive one for your son!