I think we have all felt pressure on the golf course at some point, regardless of handicap level. Pressure is created when we have expectations for how we should perform, and generally increases when we start thinking more about the result (or possible results) of our coming shot.
What this really means is that we are either thinking in the past (as in, the last time I played this shot, I hit it in the water or in the trees) or thinking in the future (as in, if I hit this shot well, I have a chance to play my best round of golf...ever...; or even worse, if I mess up this shot, I will lose any chance of winning this match...).
There are many different ways that a golfer can try to deal with pressure at the tough moments on the golf course. Many teaching pros will talk about the importance of a pre-shot routine, arguing that by going through the familiar routine, you will be more likely to focus on the present and just make a good swing. But in my view, this is only a technique or a tool that one can use, and doesn't get to the root cause of why we sometimes fail to perform when we feel more pressure. Ultimately, we don't train ourselves on each and every shot to make our best swing possible, and we only focus on trying to do it under pressure. And if you don't train consistently, how can you expect to do it when you are under pressure?
There is a method I heard about in a podcast that I listen to that addresses this which is appropriate enough called NATO Golf: Not Attached to Outcome. (link to the podcast is below)
If you don't have time to listen to the podcast, the basic theory is to keep score a different way when you next play golf. For every shot, you rate yourself on two things:
1) Did I select the correct shot needed given the situation?
2) Did I execute the shot that I selected well?
For the first question, you are asking yourself whether you picked the correct club, whether your pitch should be a low bump-n-run or a high chip shot that lands soft. Whether, for those that try to shape shots, you should hit a fade or a draw, or whether you want to hit a low or a high shot. This first question is all about assessing the situation for the shot and making the right decision for what you are going to do and then committing to it.
Then the second question is fairly simple. Did you execute the shot that you decided based on the first question? It doesn't matter if the ball didn't get over the tree, or went running well past the hole; did you execute the shot?
Your score then is not the number of strokes on a hole; you can use smiley faces for when you make the right decision and for when you execute your intended shot. Or check marks and X's if you prefer. You're goal is simply to have as many smiley faces or check marks as possible. For every shot, you have the chance for two smiley faces or check marks.
For example, say you decide to hit an 8 iron over a tree, or you decided to hit a bump and run to a pin in the middle of the green. If the ball didn't get over the tree, but you hit the ball well, then that would be an X (or un-smiley face) for the decision, but a check mark (or smiley face for execution). Or conversely, if you bladed your 8 Iron right into the tree, it might be a check mark for the decision and an X for execution. As for the bump-n-run, say that the ball went running well past the hole on the chip because it was sloped more than you expected, but you executed the shot correctly, then that means you didn't make the right decision on the type of shot.
The next time you play, perhaps give this a try; it might make you approach each shot differently and might give you a tool you can use when you get to the longest drive hole or closest to the pin to give it your best shot!
(Note that in the podcast, they mention an app you can use to score the way they recommend; that app doesn't work outside of the USA at the moment, but you don't need the app to try the approach.)