Romans 13:1-7 is a text that is too important to misunderstand. The text has been used to justify the authority of tyrants and as supposedly revealing a general Christian doctrine in favour of a legitimate state authority. By implication it supposedly supports a general Christian doctrine in favour of the legitimate use of legal and judicial coercion to repay wrongdoing here on earth.
This kind of use of the text leads to a range of unnecessary problems.
Firstly, there is no other text in the New Testament in favour of the state as a legitimate authority established by God ‘under Him and over the people’, and there are a good many texts associating coercive authority as the manifestation of Satan’s domain rather than God’s. Furthermore, Jesus claimed ‘All authority in heaven and on earth’ (Mat 28:18), and the Paul affirmed but one Lord (1 Cor 8:6, Eph 4:5).
Secondly, there is nothing in the text or anywhere else in the canon that can be used to refute the application of the text to support the use of state power against heretics as, for example was maintained by Augustine and as practiced in the name of Jesus Christ for centuries.
Thirdly, it flies in the face of reality. State power is not actually used in the manner apparently described, and it is frequently used in just the opposite manner: to reward the well-connected evildoers and to punish the good people who have been unfortunate enough to encounter state officials raising revenue, expanding territory or otherwise imposing their wills and the policies of state on everyone else. The promise of freedom from fear of the one in authority is a promise broken so frequently and conspicuously as to make an ironic reading almost forced.
These problems, and there are others like them, are unnecessary problems because they are based on an approach to the text that goes against everything the context suggests that it means. We need to start the interpretation process again by getting back into the context – historical, prophetic, theological and polemical – that the text was written in.
See here for a paper presenting this approach
 Westminster Confession of Faith, Chapter XXIII, Of the Civil Magistrate, enlisting Romans 13:1-4 and 1 Pet 2:13 as proofs. 1 Pet 2:13 does not say that governors are under God, is says they are under the Emperor.
 E.g. Mat 4:8-10, Eph 6:11-12.
 As argued in The Irony of Romans 13, T.L Carter.