If you have more herbs than you can realistically use within a few weeks, freezing is a better option than trying to keep them fresh indefinitely. Chop the herbs, place them in an ice-cube tray and cover with water or a little oil. Once frozen, transfer the cubes to a freezer-safe container or bag. Frozen herbs will not have the same crisp texture as fresh leaves, so they are better suited to curries, dals, chutneys, marinades and cooked dishes than garnishing.
For fresh coriander and mint, think hydrated stems, dry leaves and controlled humidity. Remove damaged leaves, avoid storing wet herbs, keep the stems supplied with moisture and check the bunch regularly.
With the right balance, that bunch of coriander or mint does not have to become a three-day refrigerator casualty. It can stay usable for significantly longer, meaning fewer wasted herbs and fewer emergency trips to the vegetable market.