Lossless extraction of streams from WebM

To extract audio from a WebM file, using the ffmpeg tool (https://www.ffmpeg.org/download.html) :

ffmpeg -i "input.webm" -vn -acodec copy "output.oga"

Explanation :
"-i input.webm" designates the input file
"-vn" removes the video stream from the output
"-acodec copy" tells ffmpeg to copy the audio stream as-is (no re-compression)
"output.oga" designates the output file.

NB : Use quotes "" around filenames that contain spaces.

The output file extension has to match with the format of the audio stream contained in the source webm file.

I use ".oga" as output file extension because most webm files I handle contain Vorbis audio.
".oga" is the prefered extension in this case, even if .ogg is still a frequently encountered extension for vorbis audio-only files.

This command line based on ffmpeg should give you the audio format from the source file :
ffmpeg -i "inputfile.ext" Search for the line containing the text "Audio", usually near the end of the command output.

In my case, this is the output :
Stream #0:1: Audio: vorbis, 44100 Hz, stereo, fltp (default)

Reading this wikipedia page might give you some insight on which file extensions should be used with which audio formats : http://en.wikipedia.org/wiki/Audio_file_format

Since WebM is a Matroska subset, mkvtoolnix should let you demux the files. It's open source, cross platform, and the author provides binaries for Windows.