which element will be returned from std::multimap::find, and similarly std::multiset::find?

The find method may return an arbitrary one if more than one is present, though your STL implementation might indeed just give the first one.

It's safer to use the 'lower_bound' method, and ++ iterate from there (see std::multimap::lower_bound). Do note though that 'lower_bound' returns a ref to another element if what you're looking for isn't present!

The C++ standard says that for any associative container a, a.find(k) "returns an iterator pointing to an element with the key equivalent to k, or a.end() if such an element is not found", and it doesn't impose any additional requirements on multimap. Since it doesn't specify which element is returned, the implementation is permitted to return any matching element.

If you're trying to imitate the exact behavior of multimap on the platform where you're running, that's bad news, but if your goal is just to satisfy the same requirements as multimap, it's good news: you can return any matching element that you want to, and in particular it's fine to just always return the first one.