In this work we present techniques for bounding the cyclicity of a wide class of monodromic nilpotent singularities of symmetric polynomial planar vector fields. The starting point is identifying a broad family of nilpotent symmetric fields for which existence of a center is equivalent to existence of a local analytic first integral, which, unlike the degenerate case, is not true in general for nilpotent singularities. We are able to relate so-called “focus quantities” to the “Poincaré–Lyapunovquantities” arising from the Poincaré first return map. When we apply the method to concrete examples, we show in some cases that the upper bound is sharp.