Ursula's Necklace is featured in the Little Mermaid, it was used to capture Ariel's voice as part of the deal to grant her legs. The movie implies that it may be a magical necklace as it is often glows when Ursula seems to start using a spell such as taking Ariel's voice or even transforming into Vanessa. On a semi-related note, there were also ghostly hands that originated from the nautilus, as evidenced when Ursula took Ariel's voice as part of the deal.
In the Broadway Musical
Although her necklace does not actually appear in the Broadway version of The Little Mermaid, a similar item known as the Nautilus was a major plotpoint in it, and it was mentioned that Ursula inherited the Nautilus from her father Poseidon on his deathbed, and with it granted enough power to rule half the sea. It was destroyed by Ariel, and took Ursula with it.
It's power versus the Trident was never stated, but Ursula exclaimed that she would use it to store items.
Close to the end of the Little Mermaid, Scuttle snaps the necklace of Vanessa's neck, helped largely by Max biting Vanessa. It falls on deck and shatters, giving Ariel back her voice.
In the Broadway version of the movie, Ariel breaks the necklace which is the source of Ursula's powers.