I use a piece of alpha release software called the Archivist. It will only archive public tweets so if anyone in your twitter stream protects their tweets, these will be missing from the archive.Download and install the software, and fire it up.
In the search box type in your query (e.g. #ukedchat) and hit get tweets. This will pull in a list of tweets (in the same way that Twitter Search does). Leave the software running if you want to gather tweets over a period of time. It will work in the background saving the tweets to disk.
When you want to save a record of the tweets, click [Export to Excel]. This will save a tab delimited file which you can import into Excel.Fire up Excel. Click open and search for your file (you may have to search for all file types so the exported file shows up).
When the import wizard comes up, tell excel the file is delimited. then on the next screen tell excel that the delimiter is a tab and hit finish.
You now have a record in Excel of all the tweets you wanted. You can sort these by the twitter id (column 1) if you mix them up for any reason. Simples!