Formal and grand:
* Majestic
* Imperial
* Sovereign
* Royal
* Kingly
* Queenly
* Princely
* Noble
Elegant and dignified:
* Stately
* Grandiose
* Distinguished
* Imposing
* Magnificent
Other synonyms:
* Stately
* Magnificent
* Splendid
* Grand
* Exalted
* Superb
* Impressive
The best synonym will depend on the specific context in which you are using the word. For example, "majestic" might be a good synonym for "regal" if you are describing a king's appearance, while "stately" might be a better choice if you are describing a building.