This paper presents a new blind carrier frequency offset estimation scheme for orthogonal frequency division multiplexing (OFDM) systems with constant modulus (CM) signaling. We consider both single-input single-output (SISO) systems and multiple-input multiple-output (MIMO) systems with orthogonal space-time block coding. The proposed scheme is based on the reasonable assumption that the number of resolvable multipaths is much smaller than the number of subcarriers, which implies that the channel frequency response on two consecutive sub-carriers is approximately the same. Based on this, we propose cost functions which minimize the difference of the signal power between neighboring subcarriers. We prove the identiflability of the proposed scheme and show that significant performance improvements with low complexity can be achieved, all relative to existing estimation schemes.