When trying to research your dishware, you need to be more specific in a search pattern. The word "Royal," for instance is used on many products including Royal Doulton, Royal Copenhagen, Royal Albert, Royal Winchester and more. Royal Doulton has produced dishware since 1815 and there are countless patterns. Today, they even produce dishware for Target.
By using the term "Royal" you could also be referencing dishware produced as souvenirs featuring the British Royal Family made to commemorate events such as coronations and weddings.
When you try to learn about what you have, read the maker's mark on the bottom. Use a magnifying glass. Describe all that you see including the full name of the company or the lettering that is shown. Also note whether the name of the company is enclosed in a shape like a circle or wreath. Look for other images in the mark such as crowns, ships, animals, etc. Makers marks sometimes change slightly over the years so that can be a clue to the item's age.
Dishware companies often made hundreds of patterns so you need to identify the pattern as well. In your search mention the basic color scheme, shape, images in the design (flowers and type, bird and type, landscapes, Asian motifs, etc), and edging.
Only when you identify and clarify what it is that you have can you decide on pricing. You can try online prices guides, check out clubs or groups dedicated to the company's products, or follow the suggestions posted in the article.