We present an application to cosmological models in f (R) theories within the Palatini formalism of a method that combines cosmography and the explicit form of the field equations in the calculation of the redshift drift. The method yields a sequence of constraint equations which lead to limits on the parameter space of a given f (R)-model. Two particular families of f (R)-cosmologies capable of describing the current dynamics of the universe are explored here: (i) power law theories of the type f (R) = R − β/R n , and (ii) theories of the form f (R) = R + α ln R − β. The constraints on (n, β) and (α, β), respectively, limit the values to intervals that are narrower than the ones previously obtained. As a byproduct, we show that when applied to General Relativity, the method yields values of the kinematic parameters with much smaller errors that those obtained directly from observations.