I know someone else says this wouldn't work, but it does. I just harvested some basil from my hydroponics and didn't have a chance to even put it in water. I came back and both my regular and my Thai basil were limp and withered up. I made a cold water bath (no ice, just cold water from the tap) with a little lemon juice in it and submerged both, leaving there a good hour. When I came back in, the sweet basil looked like it had just been picked. The Thai basil had very slight edge browning, but still looked a lot better, and totally usable. I pulled and dried them, then had to leave again before using them and the same thing happened. I just threw both back in the water bath, and they still look great. I can't detect any change in the taste, either, after rinsing the lemon juice off.
I know the best way to keep fresh basil is not to refrigerate it: just put the stems in some water and keep it on a warm counter until you use it. Change the water out every day and it will keep a long time. The basil I harvested is going into the freezer, and I plan to try a few different techniques so I can see what works best. I know Ina Garten says she just processes hers in the food processor with water, dumps it in ice trays and tops the cubes with olive oil to keep it from oxidizing. I think I'll process mine with a little lemon and water, then do the same thing.
BTW, I've never been able to grow anything but lime basil until I turned to hydroponics. It is the easiest gardening I've ever done, uses a lot less water than regular gardening, and the basil grows like wildfire. The reason I harvested these is they were three feet tall and taking over the room. From two sweet basil plants I got enough basil that it would have cost at least a hundred dollars to buy in the store. The Thai basil would have been at least 70 dollars, and I only had the one plant to harvest from. This is the cheapest way to grow your own herbs and you can process and put up the extra for cooking, plus you always have fresh on hand for salads and sandwiches and such. I really recommend it. Heck, you could probably sell the excess, if you wanted, and even MAKE money on it!