The phrase "silent vigil" means to stay quiet and watchful, usually as a way to show respect, honor, or remembrance for something or someone. Full definition
Members of the group, frustrated by the Francis report's refusal to call for specific individuals to pay the price for the failures, will stand in silent vigil outside the NHS Commissioning Board's offices in Manchester on Thursday. (politics.co.uk)
At bedtime, stick to a peaceful routine — a shower or bath, a gentle story or a few poems (or 15 minutes of independent reading), and maybe a song and a couple of minutes of silent vigil with you sitting by the bed. (babycenter.com)
I had never spent time with a person in that way, in keeping a silent vigil with him, in just being there with him when he couldn't respond. (firstthings.com)