4:3 footage to 1:9

I don't know if this is the right place for this question but suppose I have some old archive footage that is naturally 4:3. I need to put this in a 16:9 sequence. Normally I would put this in a frame to preserve the quality but I notice on some programmes they have managed to make it 16:9 size and keep the quality. Is this done by some clever computery means? What would be the ideal way of doing this (while not just blowing it up to 33%)?
Thanks