I did something like what you're after once, and while it's possible to get some level of reflection and access to higher-level features, the maintenance headache might not be worth it. My system was used to keep the UI classes completely separated from the business logic through delegation akin to Objective-C's concept of message passing and forwarding. The way to do it is to create some base class that is capable of mapping symbols (I used a string pool but you could do it with enums if you prefer speed and compile-time error handling over total flexibility) to function pointers (actually not pure function pointers, but something similar to what Boost has with Boost.Function--which I didn't have access to at the time). You can do the same thing for your member variables as long as you have some common base class capable of representing any value. The entire system was an unabashed ripoff of Key-Value Coding and Delegation, with a few side effects that were perhaps worth the sheer amount of time necessary to get every class that used the system to match all of its methods and members up with legal calls: 1) Any class could call any method on any other class without having to include headers or write fake base classes so the interface could be predefined for the compiler; and 2) The getters and setters of the member variables were easy to make thread-safe because changing or accessing their values was always done through 2 methods in the base class of all objects.
It also led to the possibility of doing some really weird things that otherwise aren't easy in C++. For example I could create an Array object that contained arbitrary items of any type, including itself, and create new arrays dynamically by passing a message to all array items and collecting the return values (similar to map in Lisp). Another was the implementation of key-value observing, whereby I was able to set up the UI to respond immediately to changes in the members of backend classes instead of constantly polling the data or unnecessarily redrawing the display.
Maybe more interesting to you is the fact that you can also dump all methods and members defined for a class, and in string form no less.
Downsides to the system that might discourage you from bothering: adding all of the messages and key-values is extremely tedious; it's slower than without any reflection; you'll grow to hate seeing boost::static_pointer_cast and boost::dynamic_pointer_cast all over your codebase with a violent passion; the limitations of the strongly-typed system are still there, you're really just hiding them a bit so it isn't as obvious. Typos in your strings are also not a fun or easy to discover surprise.
As to how to implement something like this: just use shared and weak pointers to some common base (mine was very imaginatively called "Object") and derive for all the types you want to use. I'd recommend installing Boost.Function instead of doing it the way I did, which was with some custom crap and a ton of ugly macros to wrap the function pointer calls. Since everything is mapped, inspecting objects is just a matter of iterating through all of the keys. Since my classes were essentially as close to a direct ripoff of Cocoa as possible using only C++, if you want something like that then I'd suggest using the Cocoa documentation as a blueprint.