Ben's solution was great but I needed to modify it a bit for me as, instead of a single text file, I wanted to save the quotes in a single Evernote note.
I've never used Keyboard Maestro before but with Ben's macro, some Googling and trial and error I managed to hack together a solutions. Here's how I modified Ben's macro:
Most of it is the same (I just changed the hot key, a personal preference), but the "Open URL:" is the key part.
For this to work, if you don't already have one, create a new note in Evernote. Also, make sure to sync Evernote at this point. To get the URL for the note, right-click on it and select "Copy note link".
Now paste this as the URL to be opened and select Evernote as the application to open it with.
I also made some minor modifications to Ben's append text:
“%NamedClipboard%Quoted text%” | saved %ShortDate% %ShortTime%
For some reason I couldn't get the appending to work properly if Evernote was not running when pasting. I have Evernote running almost constantly so it's not an issue for me but if you know how to fix this, let me know!
You can find more great articles on Ben's Keyboard Maestro series.