"Your Majesty" is used when speaking directly TO the royal person.
Servant speaks to King or Queen:
"Excuse me, Your Majesty, may I bring you some tea?"
"His Majesty" or "Her Majesty" is used when speaking ABOUT the royal person.
Servant to kitchen staff:
"The King would like his tea now. Will you take some to His Majesty?"
or
"The Queen would like her tea now. Will you take some to Her Majesty?"
I am actually not sure which of these words should be capitalized (her majesty or Her Majesty), since this is not a usage I'm very familiar with. We have no majesty in the USA! :)