Perhaps a better question is, how big is big?
Several designs we've been considering have a pair of diodes to discharge the test capacitor and limit the circuit voltages, but I've heard these can fail with large, charged capacitors.
I think the issue isn't necessarily how high the voltage (tube amplifiers get to hundreds of volts), or how high the current delivered, but how much energy is going to be dissipated in the protection components that discharge the guilty capacitor.
I'd say the answer is, the size of two fists. I think we're talking about ~ 100J of energy. Isn't that more than enough to blow out a common glass diode and/or a 1/4-watt resistor?