This is a common issue when e-mailing or uploading video files.
One note is that you should make the filesize you choose below about 20% smaller than you need. For example I took a 219MB video and told it to be 20M. The resulting file was still about 21.9M but it was OK when I said 18M and was barely below the 20M size.
ffmpeg is our friend here, just use this command:
ffmpeg -i TheLargeVideo.mp4 -fs 100M TheLargeVideo-resize.mp4