There are two classic examples of this phenomenon: the declaration of war requirement and gold and silver as legal tender.
Article 1, Section 8, enumerates the powers of Congress. It states in part: "Congress shall have Power To declare war."
Article 2, Section 2, enumerates the powers of the president. It states in part: "The President shall be Commander in Chief of the Army and Navy of the United States."
Thus, while the president is given the power to wage war, he is not given the power to declare war. The decision on whether to go to war lies with Congress. Unless Congress declares war, the president is constitutionally prohibited from waging war.
Yet, we all know that presidents ignore this constitutional restriction with impunity. They exercise both the power to declare war and wage war. There has never been a constitutional amendment authorizing this revolutionary change in our governmental structure.