Compensating the Group Delay of an Analog Filter using DSP
It's often easier to design FIR filters for compensating group delay. At the same time they could also compensate the magnitude if necessary. The easiest method is to use a complex least squares method, which boils down to solving a system of linear equations for the filter coefficients.

The difficult part is to choose an appropriate bulk delay in the definition of the desired phase response. A good starting point is to choose the average delay to be close to half the filter length.

Take a look at this answer for an example of FIR group delay equalization.

You can use the Matlab/Octave function lslevin.m for designing FIR filters with prescribed magnitude and phase responses.