What to do if your opponent Singed proxies?

I farm 1-2 waves then go and kill him when he is low. Just keep track of his health, if you have a ranged targeted ability you can snag him between waves. Malphite works wonders because he can slow him down and his passive lets him tank the minions easily enough.

If he just proxys your lane I'd just farm and ignore him as well tell my jungler to ignore him.

If he double proxies however you got to deal with him, as it has quite an impact on your other lanes.