Speaking on purely philosophical conservative terms, we first need to make a distinction between the European and American Conservatism, which are fundamentally different. As stated, Conservatism is about opposition to quick and radical change, however, it's important to make a distinction in Europe, that tends to favor monarchy and aristocratic institutions. The United States was fundementally opposed to monarchal institutes, so modern American Conservatism has more in common with liberal (Classical Liberalism, Liberalism, and NeoLiberalism to the non-American World, as described in various points in Wikipedia). It is in this sense that Modern American Conservatism is conservative to Americans: The tenants of the nation was that governments exist by consent of the govern, individualism, and that local governments should have more power to interfere with individuals than state governments, which should have more power than the national government (Jeffersonian Democracy). Keep in mind that at its time, Conservatives were opposed to the revolution (Called Loyalists at the time). Over time, support of England government lost support, seeing its death knell during the War of 1812. By the time of the Civil war, the political divide is about how much power should be given to various levels of government in a federal system (a debate which still rages).
As to your question, the American Conservative can justify the Revolutionary war by means of support of classical Liberal Ideology, under which, a government derives power from the consent of the govern. You need not look father than the opening line of the Declaration of Independence, which explains that a government that loses consent of the people has lost its power and returns it to the people. This is further supported by the Second Amendment (right to keep and bear arms) and Federalist Paper Number 46 (James Madison) explained that it was a sign of trust by the government that it let it's citizen keep arms and that the people need not fear the government because the people were armed.
Modern Conservatives are very supportive of the Second Amendment and the US has the highest gun ownership in the world both in numbers and per capita (350 million guns compared to a population of 330 million citizens). Many second amendment supporters do hold with the intent as expressed by Madison in that the 2nd Amendment is an unofficial "Fourth" check on the government, and that should government not correct it's over reaches, an armed citizenry will correct the over reach. In such a situation, the idea of "Consent of the Governed" holds that the government only has its power if the people say it does, and any government that loses the support of the people is no different than any other threat, which the people have a right to defend against. This gets a lot of ridicule from non-conservatives in the United States, but any serious discussions regarding repeals of the second amendment will run into the problem of safely confiscating fire arms from a population that does believe in this right (hence why non-conservatives try to make weapons procurement more difficult but only hardliners discuss out and out banning of it).