The elastic contact of non-ideal conical and Berkovich indenters with bi-layer half-spaces is investigated. Blunted tips are simulated as smooth surfaces. The boundary element method is employed to carry out the numerical simulations of nanoindentation. An analytical analysis of the influence of the coating thickness and the tip bluntness magnitude on the nanoindentation loading curve is realized. The dimensionless compression force is introduced in order to describe the nanoindentation at different approaches between the indenter and the coated half-space. A practical technique for determining the Young's modulus of coatings is proposed. The technique is based on the modelling of indentation of the blunted indenter tip into the coating/substrate composite. This technique is applied to the nanoindentation study of nanocrystalline Cr coatings on silicon and glass substrates being tested by a diamond Berkovich indenter with a blunted tip.