We study theoretically the local absorption spectra of single and double semiconductor quantum dots (QDs), in the linear regime. The three-dimensional confinement leads to an enhancement of the Coulomb correlations, while the spectra depend crucially on the size of the ‘local’ probe. We show that because of such Coulomb correlations the intensity of certain optical peaks as a function of the resolution can exhibit an unexpected non-monotonic behavior for spatial resolutions comparable with the excitonic Bohr radius. We finally discuss the optical near-field properties of coupled QDs for different coupling strengths.