I am especially interested in Northern France between the 9th and 13th centuries, but the question stands for other centuries and other parts of the world : how were borders between two states (or equivalents at the time) drawn in Medieval times ?
Did they follow rivers (if so were they to be significant rivers, as in navigable ones) ? Mountains (if so did they follow summits, crests...) ? Valleys (even without rivers) ? Other geographical features ? Did they follow already established borders, such as old Roman Empire provinces ? Or borders that were still relevant, such as Catholic church dioceses ?
Or was it somewhat random (as in "so this river is ours, this river is yours, and the border is somewhere in between") ?
Although I am not qualified to answer your full question I can say this:
In the Angevin and Capetian France around the 1100s there was an influx in castle building due to the constant fluctuation of borders. Particularly around Upper Normandy and the Eastern Vexin (So like around Rouen.) Both realms built, literally, a line of castles stretching from the Vexin all the way down to Western Aquitaine. If you look at a map of medieval France you will clearly see a border drawn from the castles. Most notably are: Chateaux Gaillard, Chinon, Chateauroux, Bouvines, and Carcassone. (although Carcassone is a much older castle dating to Charlemagne's time.)
Stone castles gave kingdoms a much better grip on their lands and borders:
Nobles can survey the land around their castle, usually from a hilltop. This allowed for better observation of the peasants working below but also any approaching raids.
Although armies can simply zip around the castle, the baron or noble of the castle would certainly have some knights inside. So even if this castle was completely isolated (assuming the moving army doesn't want to waste time besieging it.) The noble could simply lead out a raid of cavalry and ruin the baggage train, pillage the enemy land (unprotected), and burn their tents. They could then return to the safety of their castle and pose an ever annoying threat.
As stated above the castle was an excellent base of operations, and it isn't going anywhere! Most castles were built to withstand a siege for 4-6 months, by that time it was usually too late for the besiegers as a relief army was headed its way. Overall castles are amazing and have superior capabilities contrary to popular belief.
Hope this helps, this relates more to early medieval but it gives you an idea of one way of keeping a border clean.
Source: The History of William Marshall:http://www.amazon.com/Greatest-Knight-Remarkable-William-Marshal/dp/006226205X/ref=sr_1_1?s=books&ie=UTF8&qid=1426820772&sr=1-1&keywords=thomas+asbridge Great Castles of Europe:http://www.amazon.com/Great-Castles-Europe-Discovery-Learning/dp/B000AXXBQ2 and knowledge gained in my free time.