The Scriptures clearly teach it is never right to render evil for evil. Vindictive retaliation is simply not a principle the Bible will support (see v. 19). To do that would be to let evil have the victory.
Keeping with the evident sense of overall Scriptural principles, what is being indicated here is that by being exceedingly kind and generous to one's enemy, that person will likely experience a burning sense of shame, remorse and regret for his wrongdoing. Consequently, the "enemy" is then likely to repent of his enmity and be reconciled.
Isn't that what Paul says in the next verse (v. 21)?
The Book of Proverbs - from where the opening quote in Romans is taken - also contains the following passage:
Consider also...
Nonetheless, Charles Bridges offers sage advice: "We are not bound to trust our enemies, but we are bound to forgive them."