The Cramer-Rao bound (CRB) gives a lower variance bound that an estimator can achieve. Presented is a mathematical approach to estimate it for specific radar signals, namely Costas signals and their modified versions. The modified versions design consists in widening Costas frequency hops and replacing rectangular pulses with other waveforms (namely linear frequency modulated pulses, phase codes and other Costas codes). The calculation is based on approximations of the ambiguity function (AF) around the mainlobe. The CRBs are then derived based on relationships between the AF and these bounds.