The fundamental limit for small antennas provides a guide to the effectiveness of designs. Gustafsson et al, Yaghjian et al, and Mohammadpour-Aghdam et al independently deduced a variation of the Chu-Harrington limit for planar antennas in different forms. Using a multi-parameter optimisation technique based on the ant colony algorithm, planar, meander dipole antenna designs were selected on the basis of lowest resonant frequency and maximum radiation efficiency. The optimal antenna designs across the spectrum from 570 to 1750 MHz occupying an area of $56mm \times 25mm$ were compared with these limits calculated using the polarizability tensor. The results were compared with Sievenpiper's comparison of published planar antenna properties. The optimised antennas have greater than 90% polarizability compared to the containing conductive box in the range $0.3<ka<1.1$, so verifying the optimisation algorithm. The generalized absorption efficiency of the small meander line antennas is less than 50%, and results are the same for both PEC and copper designs.