R[oman|everse] Polish Notation
Python 2 + roman, 118 bytes

from roman import*
s=[]
for i in input().split():s+=[eval(s.pop(-2)+i+s.pop())if i in&quot;+-/*&quot;else`fromRoman(i)`]
print s

Demo
It cannot be tested online because of the module it makes use of, but you can see how  to run this here (a full program accepting input from STDIN – an expression with quotes – and printing the output to STDOUT – in the form of a list, the stack). Uses a slightly older version, because I won't bother to create a new GIF for only a few bytes:

To install the package, you can run the following in the Terminal / Command Line:
pip install roman