Prepare In Advance
Sooner or later you'll receive a late night call requesting support. Consider having remote access control software installed on your assigned test systems, if your organization allows it. Remote access software allows you to personally interact with the test system. You can check configuration files, databases, arguments, software setup, etc. This might reduce the length of time required for you to decide if the issue can be resolved remotely or require an onsite visit.
Lessons Learned
A good practice is to capture any lessons learned within 24 hours of a late night support call. Specifically focus on ensuring that the same issue doesn't recur; that support has sufficient training, resources, and know-how on resolving the issue; that you identify what resources you personally need in the future to increase your effectiveness on future calls for different issues.