A multi-antenna (MIMO) system with eavesdropper is studied, where the transmitter has no perfect knowledge about the channel to the eavesdropper. The transmitter only knows that the channel matrix of the eavesdropper is drawn from a certain set. For this scenario, the worst-case secret key rate and the worst-case channel matrix of the eavesdropper are characterized. It is shown that the maximization of this rate under a sum power constraint at the transmitter is a saddle point problem. Upper and lower bounds for the maximized worst-case secret key rate are derived. Strategies for the high and low SNR regime are presented and the results are finally illustrated and discussed in comparison with the maximized worst-case secrecy rate.