Yes, there were other areas that voted against secession but were less successful than West Virginia was in their resistance. The most notable example other than West VA is East TN. Tennessee, as a whole, had two votes for secession. The first did not pass, as representatives from east and middle TN voted against secession, while those in west TN voted in favor of it. Following Fort Sumter, a second vote was held, where the results were more in favor of secession. Middle TN shifted to be in favor of secession in the second vote while east TN continued to resist secession. This continued to the point that East TN held a convention in favor of breaking away from TN and forming their own state which would remain in the Union, much like West Virginia was doing at the same time.

However, East Tennessee was a key location for the Confederacy because it contained rail lines running through Chattanooga which would connect the Eastern and Western sections of the Confederate States. If they let East Tennessee go, they would be seriously limiting their mobility by cutting off their access to those rail lines. So, the TN state legislature refused and Confederate troops were stationed in that part of the state for the remainder of the war to prevent East TN from rejoining the Union. Notably, the rail lines, and in particular the bridges, became a target for pro-Union residents of East TN. They would burn the bridges in order to prevent Confederate forces from using them.

It's important to note that East TN wasn't alone in being against secession, it was just the other biggest area of resistance outside of West VA. I like to link county vote maps like this one to illustrate the lack of support in many areas of the south. North Alabama and North Georgia are known as other notable places of resistance to secession. The common thread between these places is they were mainly made up of people the Appalachian mountains, where the land wasn't well suited to the large plantations that existed elsewhere in the south. As a result, not only did most people in those areas not own slaves, but they didn't really interact with many people who did, so it wasn't an issue that was important enough for them to want to break away from the US. Most weren't outright abolitionists, they just really didn't have strong feelings on the issue one way or the other.

As for how they would resist, one of the biggest ways, especially in areas that fell under Union control early in the war (including much of Tennessee, men would enlist in Union regiments. They typically served both as scouts (because they knew the areas better than northern soldiers) and guards who would protect areas that the Union had retaken from falling back into Confederate hands. According to the book Lincoln's Loyalists, by the end of the war, over 100,000 southerners had enlisted in Southern Union regiments and every southern state except South Carolina produced at least one Union regiment.

I answered a question similar to this, about southerners fighting the Confederacy several months ago in this thread. It's not specifically what you asked, but I'll include the link since it's somewhat related. Let me know if you have any other questions. I need to get back to work at the moment, but it's one of the random points of history I'm very interested in, so I've read a good deal about it.