You can't sustain a voltage of 9V, as soon as the power is removed the voltage from the cap will start to drop so you have to list what your limits are, if 9 volts is your lower limit then you have to chose an upper limit then you can calculate the time it would take the capacitor to discharge from the higher state to the lower one, the brightness of the LED will gradually fade, and the capacitance is going to be pretty high. I don't like the math myself which is why I use a simulator. If you start with a 10V charge and discharge to 9V you'll need about 3/4's of a farad worth of capacitance to last 3 minutes, mind you you'll get MANY MANY more minutes of gradually dimming light, depends on exactly what you need. If you're talking about running the LED down to just barely visible you can get away with a much lower capacitance.