This work uses both simulations and experiments to study helium plasmas (99.999% purity), sustained by surface-wave discharges (2.45 GHz frequency) in capillary tubes (3mm in-radius) at atmospheric pressure. The simulations use a self-consistent homogeneous and stationary collisional-radiative model (CRM) that solves the rate balance equations for the different species present in the plasma (electrons, He+ and He(+)2 ions, He(n <= 6) excited states and He-2(*) excimers) and the gas thermal balance equation, coupled with the two-term electron Boltzmann equation (including direct and stepwise inelastic and superelastic collisions as well as electron-electron collisions). The experiments use optical emission spectroscopy diagnostics to measure the electron density ne (from the H-beta Stark broadening), the gas temperature T-g (from the ro-vibrational transitions of OH, present at trace concentrations) and the populations of excited states in the energy region 22.7-24.2 eV, whose spectrum allows determining the excitation temperature T-exc. Measurements yield ne similar or equal to (2.45 +/- 1.4) x 10(13) cm(-3), T-g similar or equal to 1700 +/- 100 K and T-exc similar or equal to 2793 +/- 116 K, for a similar to 180 +/- 10 W power coupled and similar to 1 cm length plasma column. The model predictions at n(e) = 1.7 x 10(13) cm(-3) are in very good agreement with measurements yielding T-g = 1800 K, T-exc = 2792K (for similar to 30% average relative error between calculated and measured excited-state densities), and a power absorbed by the plasma per unit length of 165Wcm(-1). The model results depend strongly on ne, and hence on the plasma conductivity and on the power coupled to the plasma. The coupling of a thermal module to the CRM has been shown to be crucial. Increasing the electron density leads to very high gas temperature values, which limits the variation range of (n(e), T-g) as input parameters to the model.