Is it possible to cast a pair<Key, Value> to a pair<const Key, Value>?

You can convert a value of type pair<Key,Value> to pair<const Key,Value>.

However, reading the question carefully, you're actually asking if, given a pair<Key,Value> you can create a pointer or reference to pair<const Key,Value> referring to the same object.

The answer is no - the only situation where a reference or pointer to one type can refer to an object of a different type is if the object type inherits from the referenced type.

One possibility is to return a pair of references, pair<const Key&, Value&>, created from the pair you wish to reference.

Yes.

std::pair<int, double> p(1,2);
std::pair<const int, double> q = p;   // no problem

//q.first = 8;  // error
q.second = 9;

int b; double d;
std::pair<int &, double &> s(b,d);
std::pair<int const &, double &> t = s;  // also fine

As Kerrek SB pointed out, you can construct std::pair<const Key, Value> from std::pair<Key, Value>. However, your original question implies that you want to avoid constructing std::pair objects each time your iterator is dereferenced.

Unfortunately, there is not a good way to do this. You may have to construct the pair object and actually store it somewhere, particular for operator->. Otherwise you have to be able to have your map actually store pair<const Key, Value> to be able to return references/pointers to it from your iterator. Basically to return a reference/pointer, it has to be stored somewhere in that form: it cannot be a temporary.

Avoid the const_cast. That's just asking for undefined behavior when you use it to cast pair this way even though it may work quite often.