By which we mean most commonly swords but also in some cases, axes, maces, spears, bows, crossbows, etc.

A character who has a magic close combat weapon cannot use other close combat weapons - he cannot have a magic sword in one hand and an ordinary sword in the other. For example, you can carry a shield with a magical weapon. No character can carry more than one magic weapon. Magic weapons always ignore any special rules that apply to an ordinary weapon of the same type. All the rules that apply are covered in the description of the weapon.