If you have genuine silver cutlery, it might be worth something. However, it is not usually easy to reclaim the silver. If it is merely silver plated, it is very difficult to remove and reclaim the silver. This also goes with a silver tea service pot. I would, however, hang onto it because the more expensive silver gets, the more cost effective it is to reclaim it (and, at such point, the more your undamaged silverware can become).
But, most silverware is not real silver these days. Unless you spent close to $800 per place setting, your silverware is probably stainless. Which is fine for eating (and it will not tarnish), but you are not getting any silver out of it.