I pretty much only 100% container garden. I have a nice set up on our front porch and on our back porch too. With things like lettuce and herbs, you can go through several plantings in a summer season and as such, end up with a ton of leftovers. Now, there's not a way I know of to save lettuce, but basil-yes!
When I've got basil ready to go, I pick it all and rinse it off in the sink under cold water. Since my herbs are grown in containers on a covered porch, and I don't use pesticides or chemicals, I only rinse.
After rinsing and shaking off, I place a couple leaves into the bottom of ice cube trays. Think about how you cook. Do you like to use a lot of basil? If you do, you might want to pack your cubes a little fuller. I vary how many leaves I put in each because we vary how much basil we use dish to dish.
Then, fill with water, press the leaves down as best you can and pop in the freezer. These will last you a long time and you'll always have fresh basil for cooking, even in the dead of winter.