There are 13 weapons from Royal Arms group to be found in the game, with 6 of them not connected with the main storyline - acquiring them is completely optional. However, you should still collect them, as those are some of the best weapons in the game - especially Shield of The Just and Star of the Rogue.
Place to acquire
Bow of the Clever
Balouve Mines dungeon
A bow increasing Magic stat by 80 points. Additionally, the weapon gains more damage as the Magic stat of the character increases.
Greatsword of the Tall
Costlemark Tower dungeon
This sword gives an enormous attack bonus and increases health points of the character by 200. Unfortunately, it decreases Spirit by 20 and resistances to Fire, Ice, Lightning and Dark by 40.
Shield of the Just
The Tomb can be found outside, above the ground (not in a dungeon), to the west of The Disc.
An extremely good shield, increasing the health points of the main character by 500, MP by 50, Vitality by 100 and Spirit by 30 points. Additionally, it increases resistances to Fire, Ice, Lightning, Dark and Shot by 10 points.
Decreases Strength by 100 points.
A perfect item to use as a supplement - you can equip it in a slot without actually using it and the weapon will still give all of the above bonuses.
Scepter of the Pious
Malmalam Thicket dungeon
A powerful weapon which increases Magic by 150 and Dark resistance by 50 points. It's a perfect choice for characters looking for additional Dark resistance, as well as those who focus on magic.
Mace of the Fierce
Rock of Ravatogh dungeon
Another powerful two-handed weapon which significantly increases health points of the character, although decreasing Shot resistance by 50 points.
Star of the Rogue
Myrlwood Forest dungeon
One of the best weapons in the game - extremely high attack modifier allows it to deal immense damage to enemies.
Additionally, the weapon increases Fire, Ice and Lightning resistances by 20 points.