Your question reminded me a lot of the story of Turandot - and there is, apparently, a 1987 movie of this tale, and a 1983 TV movie, either of which might fit your timeline.
In the story, there is indeed a cruel princess in china, the named Turandot, who sets her suitors with three riddles, with those who failed being executed - the quote I recall is, "There are three riddles but only one death". The main character, a prince, manages to guess the answer to each of the three riddles, and when she's horrified at being forced to marry him, he issues a counteroffer - that if she can find out his name, he will let himself be executed. She has the whole kingdom looking for the answer, and tortures his slave girl to find his name (the girl refuses, and kills herself, because she is loyal and a bit in love with the prince). In the end, the prince gives Turandot his name so she can make her own choice, and she chooses to name him her love (and marry him) instead of announcing that she had indeed found his real name and having him executed. It looks like both movies were live action, and in color (at least, It looks that way from the listings I see).
Things that fit less well - I don't recall a character of a witch or a specific mention of an old man with an amulet, though there is a secondary female character of a slave girl (who gives advice and sacrifices herself for the prince), and either the ministers or the king might have some kind of amulet which I am unaware of. It might not be the movie you were thinking of, if the witch and amulet were really central to your movie - but it looked similar enough I thought I'd offer this as a possibility.