I have a high-performance software server application that is expected to get increased traffic in the next few months.
I was wondering what approach or methodology is good to use in order to gauge if the server still has the capacity to handle this increased load?
I think you're looking for Stress Testing and the scenario would be something like:
Create a load test simulating current real application usage
Start with current number of users and gradually increase the load until
whatever comes the first
Depending on the outcome you either can state that your server can handle the increased load without any issues or you will come up with the saturation point and the first bottleneck
You might also want to execute a Soak Test - leave the system under high prolonged load for several hours or days, this way you can detect memory leaks or other capacity problems.
More information: Why ‘Normal’ Load Testing Isn’t Enough