A good solution for await in try/catch/finally?

You can move the logic outside of the catch block and rethrow the exception after, if needed, by using ExceptionDispatchInfo.

static async Task f()
{
    ExceptionDispatchInfo capturedException = null;
    try
    {
        await TaskThatFails();
    }
    catch (MyException ex)
    {
        capturedException = ExceptionDispatchInfo.Capture(ex);
    }

    if (capturedException != null)
    {
        await ExceptionHandler();

        capturedException.Throw();
    }
}

This way, when the caller inspects the exception’s StackTrace property, it still records where inside TaskThatFails it was thrown.