Another clipping method is to use the pen tool. You’ll still outline the item just like with the brush method, but this time you won’t need to worry about issues stemming from using a brush tool such as opacity and feathering. To make the lines curved, click where you want the point to be then drag to give you the curve handles. When you are done you can use the Direct Selection tool to adjust the points and curve handles until you are happy with the result. Once you are done you can apply the path as a mask to the image (some programs may require you to fill the path which you can then apply to the mask.)
One thing I do want to point out – in the original photo the item looked fine, but once it was clipped the reflection of the yellow really stands out. This illustrates the importance of desaturating sterling silver items completely when they are clipped out.
Auto Select or Auto Clipping
We generally don’t use these editing tools on jewelry items due to the fact that jewelry tends to reflect its surroundings and therefore the program has a hard time distinguishing what is jewelry and what is background. This option could work on dark or patinaed silver or non-silver jewelry that is photographed on a light background as long as there are distinct edges (aka no reflections blending into the background).