We report measurements of the microwave surface impedance of the borocarbide family of superconductors LnNi2B2C (Ln=Y, Er, Tm, Ho). The experiments enable direct measurements of the superfluid density, and are particularly sensitive to the influence of magnetic pairbreaking. In HoNi2B2C the antiferromagnetic transition is clearly observed at zero field, and leads to a drastic reduction of the superfluid density, which recovers at lower temperatures. In ErNi2B2C the antiferromagnetic transition is not seen in zero field data. Magnetic effects are responsible for anomalies in the low temperature surface impedance below approximately 4K in HoNi2B2C and TmNi2B2C. The temperature dependence of the microwave impedance disagrees with simple BCS calculations.