1
I had the honour to meet my football idol.
I had the honour of meeting my football idol.
Use have the honour of + noun/-ing: ‘I had the honour of meeting the president.’
2
Would you make me the honour of dancing with me?
Would you do me the honour of dancing with me?
Use do someone the honour of + -ing, not make someone the honour.
This is a formal expression, although it can also be used humorously.
Check our coomplete grammar lesson on the difference between do and make.