Does the C++ standard library have a set ordered by insertion order?

Instead of making a std::set of whatever type you're using, why not pass it a std::pair of the object and an index that gets incremented at each insertion?

No single, homogeneous data structure will have this property, since it is either sequential (i.e. elements are arranged in insertion order) or associative (elements are arranged in some order depending on value).

The best, clean approach would perhaps be something like Boost.MultiIndex, which allows you to add multiple indexes, or "views", on a container, so you can have a sequential and an ordered index.