This paper proposes a design and fine-tuning method for mixed electric and magnetic coupling filters. It derives the quantitative relationship between the coupling coefficients (electric and magnetic coupling, i.e., E_C and M_C) and the linear coefficients of frequency-dependent coupling for the first time. Different from the parameter extraction technique using the bandpass circuit model, the proposed approach explicitly relatesE_C and M_C to the coupling matrix model. This paper provides a general theoretic framework for computer-aided design and tuning of a mixed electric and magnetic coupling filter based on coupling matrices. An example of a 7th-order coaxial combline filter design is given in the paper, verifying the practical value of the approach.