In the recent paper entitled "Explicit constructions of MDS self-dual codes" accepted in { IEEE Transactions on Information Theory}, doi: 10.1109/TIT.2019.2954877, the author has constructed families of MDS self-dual codes from genus zero algebraic geometry (AG) codes, where the AG codes of length $n$ were defined using two divisors $G$ and $D=P_1+\cdots+P_n.$ In the present correspondence, we explore more families of optimal self-dual codes from AG codes. New families of MDS self-dual codes with odd characteristics and those of almost MDS self-dual codes are constructed explicitly from genus zero and genus one curves, respectively. More families of self-dual codes are constructed from algebraic curves of higher genus.