We report on room temperature ferromagnetic resonance (FMR) studies of [ t Co|2t Ni]  × N sputtered films, where 0.1 ≤ t ≤ 0.6 nm. Two series of films were investigated: films with the same number of Co|Ni bilayer repeats (N = 12), and samples in which the overall magnetic layer thickness is kept constant at 3.6 nm (N = 1.2/t). The FMR measurements were conducted with a high frequency broadband coplanar waveguide up to 50 GHz using a flip-chip method. The resonance field and the full width at half maximum were measured as a function of frequency for the field in-plane and field normal to the plane, and as a function of angle to the plane for several frequencies. For both sets of films, we find evidence for the presence of first and second order anisotropy constants, K₁ and K₂. The anisotropy constants are strongly dependent on the thickness t, and to a lesser extent on the total thickness of the magnetic multilayer. The Landé g-factor increases with decreasing t and is practically independent of the multilayer thickness. The magnetic damping parameter α, estimated from the linear dependence of the linewidth ΔH, on frequency, in the field in-plane geometry, increases with decreasing t. This behaviour is attributed to an enhancement of spin-orbit interactions with decreasing Co layer thickness and in thinner films, to a spin-pumping contribution to the damping.