Retired English Teacher
There is an important annual rite for the Chinese. On Tomb Sweeping Day, family members go to their ancestors' tomb, sweep it, offer sacrifices like food, tea, wine, or flowers, burn joss sticks and pray to their ancestors. Do we say they worship or honor their ancestors?
Without knowing the specifics of the actual ritual, I can't make an educated answer but I would say that "honour" sounds better to me.
Note the difference in spelling:
Honour = BrE
Honor = AmE