I increased the core clock setting from the stock 880 to 1200 MHz using Afterburner. I didn't touch the voltage setting for fear of blowing the thing up.
I didn't see any increase in the performance of Crysis (~30 FPS @ 1920X1080 very high details) My evaluation is not very quantitative, as the benchmark utilities I've run won't summarize results for some reason. I'm estimating average frame rate by the FPS values while running.
I don't know If the card is actually running at 1200 Mhz. Do I need to increase the core voltage (I'm a novice and paranoid), or is this as good as it gets?
Download CPUID GPU-Z to monitor the clock speeds to see if it is really running at those settings.Also a good benchmarking and stress testing program for GPU's is MSI Kompbuster.It should have came with MSI Afterburner but if it didn't you can download it at MSI's website somewhere.
I would think you would need some voltage increase to achieve a 300mhz increase but don't touch the voltage unless you need to.Find out whats going on before you mess with the voltage.
That overclock is likely going to be unsuccessful. You should remember that the reference core clock for a 560 Ti is 822MHz, so you've already got a good head start.
A lot of factory-overclocked 560 Ti cards clocked at 950-1000MHz are failing to maintain those overclocks. You might get lucky and get that speed with increased voltage. The 560 Ti's power system can handle a small boost in voltage. You'll also need to speed up your GPU fans to offset the extra heat using the fan graph in Afterburner. Click the Settings button and then the Fan tab.