The Sermon on the Mount and Caesar's Sword

As I call Christians to the practices of radical forgiveness and nonviolent peacemaking that Jesus embodied and most clearly sets forth in the Sermon on the Mount, I often encounter Christians using Romans 13 as a kind of rebuttal. Their argument goes something like this:

“God has ordained the government and has given it the sword to execute vengeance; therefore we cannot be opposed to war because Romans 13 sanctions ‘Just War.’”

But this is an egregious misinterpretation and misapplication of what Paul is talking about.