The capacity of a cellular multiuser MIMO system depends on various parameters, for example, the system structure, the transmit and receive strategies, the channel state information at the transmitter and the receiver, and the channel properties. Recently, the main focus of research was on single-user MIMO systems, their channel capacity, and their error performance with space-time coding. In general, the capacity of a cellular multiuser MIMO system is limited by additive white Gaussian noise, intracell interference from other users within the cell, and intercell interference from users outside the considered cell. We study one point-to-point link, on which interference acts. The interference models the different system scenarios and various parameters. Therefore, we consider three scenarios in which the noise is subject to different constraints. A general trace constraint is used in the first scenario. The noise covariance matrix eigenvalues are kept fixed in the second scenario, and in the third scenario the entries on the diagonal of the noise covariance matrix are kept fixed. We assume that the receiver as well as the transmitter have perfect channel state information. We solve the corresponding minimax programming problems and characterize the worst-case noise and the optimal transmit strategy. In all scenarios, the achievable capacity of the MIMO system with worst-case noise is equal to the capacity of some MIMO system in which either the channels are orthogonal or the transmit antennas are not allowed to cooperate or in which no channel state information is available at the transmitter. Furthermore, the minimax expressions fulfill a saddle point property. All theoretical results are illustrated by examples and numerical simulations.