The descendant organizations (for example, Sons of Union Veterans, Sons of Confederate Veterans) have medals for various things but service members (active, reserve, or national guard) do not or cannot receive medals for ancestor's service during the Civil War from the Department of Defense. You would have to check with the SUV or SCV for eligibility requirements for medals from those organizations.
I hope this provides clarity.
Respectfully,
Gerald D. Hodge, Jr.
Lieutenant Colonel, U.S. Army