High frequency [1-500 MHz] measurements of the magnetoimpedance (MI) of glass-coated Co69.4Fe3.7B15.9Si11 microwires are carried out with various metal-to-wire diameter ratios. A twinpeak, anhysteretic behaviour is observed as a function of magnetic field. A maximum in the normalized impedance, ∆Z/Z, appears at different values of the frequency f , 125, 140 and 85 MHz with the corresponding diameter ratio p = 0.80, 0.55 and 0.32. We describe the measurement technique and interpret our results with a thermodynamic model that leads to a clearer view of the effects of p on the maximum value of MI and the anisotropy field. The behavior of the real and imaginary components of impedance is also investigated; they display a resonance that becomes a function of the DC field HDC for values larger or equal to HK the circumferential anisotropy field for each p value. These results are interpreted in terms of a rotation model of the outer shell magnetization.