The effects of a static contact angle θ0 on the natural frequencies of inviscid gravity-capillary waves depend on the contact-line conditions. The cases of free-end and pinned-end edge conditions are analyzed in the limit of large Bond number B. The ratio (ω2−ω02)∕ω02 (where ω0 and ω are the natural frequencies without and with meniscus, respectively) is proportional to B−1 or B−1 in the case of fixed contact angle or fixed contact line, respectively, and then the effect of the meniscus is greater for pinned-end edges than for free-end ones. When the contact angle is fixed (and for circular cylinders of aspect ratio not small) the natural frequency ω increases with increasing contact angle. When the contact line is fixed the natural frequency ω is smaller than ω0 in both cases of hydrophilic (θ0<π∕2) and hydrophobic surfaces (θ0>π∕2). It is shown that the reduction in frequency due to the meniscus can exceed the reduction associated with viscous effects. The results of this work compare better with experimental measurements, than those reported in the literature previously.