One of Microsoft's new interns took to the Azure blog yesterday to announce performance counters for Azure Web Apps. Previously, the functionality has been unavailable on the Azure portal, as the apps don't run on their own machines.
Features and Drawbacks
The new performance counters provide much of the same data as performance monitor on the desktop. A solution has been added to Application Insight's SDK Labs to pull in data and visualize it.
Metrics collect memory usage, processor load and all of the usual performance data. If that's not enough, however, the Azure web portal now supports custom performance counters. This gives more precise insights such as a thread handle count.
Unfortunately, the custom counters are limited by the data supplied by the Azure Web Apps team. However, you can get started yourself by editing the ApplicationInsights.config file.
Another drawback is the focus on historical data. At the moment, real-time monitoring is not possible, somewhat limiting the service. Microsoft is planning on implementing Live Metrics Stream in the future, but there's no word on when just yet.
You can begin using the new counters immediately via the Azure Portal. The project's GitHub page reveals the necessary information to get started. You can also use the repository here for issues and feature requests, and give feedback on the forum thread.