The hunting strategy works, but can be tedious, so often it's best to just do your thing instead of following the enemy guerrilla troops. Make sure you have enough troops following him to destroy him, or he will simply retreat after battle and you will have to go over it again. Sooner or later he will move to a position where you can move into his location quicker than he needs to get out of it, so he will be trapped.
Repeat this and you will reach him after a few provinces, because the travel time between provinces is not constant, but based on the terrain. The second your troops reach the province, stop the time and give order to move to the new location of the enemy. He will move out once he sees you coming, but don't change your path!. 
Those nations will have a limited independence, will be able to build their own army and navy, and will support you in the wars you may fight, aswell as continue colonization efforts.
Move your troops into the province the enemy is in. In EU4, when colonizing American regions (Plus Australia and New Zealand), you will form Colonial Nations after having colonized a certain number of provinces (five). If you really want to destroy those annoying troops in your provinces, it is tedious but possible. Most of the time holding a certain province or the enemy capital will give you a ticking warscore, i.e. He might get one or two of your provinces, but if you have more troops, you should make enough warscore to enforce your demands. Just capture his provinces, spread out your troops so you are able to siege multiple provinces at once. When the enemy plays a game of cat-and-mouse with you like that, where he has a small force in your country evading your troops, you basically have two choices:
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