The blooms last longest on the plant. However, I do pick some to place a bouquet on my kitchen table. To make their beauty longer lasting, I dry the flowers. They dry to make lovely bouquets for the house.
To dry them, I bind a few stems together with a rubber band. The rubber band will hook nicely from a door knob or other hanging place. With the flowers hanging upside down the peonies dry to ensure that their blooms will stand erect in a vase. After the drying I have a special bouquet that lasts for weeks or months. Give it a try sometime. Other flowers and herbs dry well this way, too.