Should I use std::shared pointer to pass a pointer?

Suppose I have an object which is managed by an std::unique_ptr. Other parts of my code need to access this object. What is the right solution to pass the pointer? Should I just pass the plain pointer by std::unique_ptr::get or should I use and pass an std::shared_ptr instead of the std::unique_ptr at all?

I have some preference for the std::unique_ptr because the owner of that pointer is actually responsible for cleanup. If I use a shared pointer, there's a chance that the object will remain alive due to a shared pointer even when it should actually be destroyed.