Electrostatic force microscopy (EFM) probes are typically coated in either metal (radius ∼ 30 nm) or highly-doped diamond (radius ∼ 100 nm). Highly-doped silicon probes, which offer a sharpened and stable tip apex (radius ∼ 1-10 nm) and are usually used only in standard atomic force microscopy, have been recently shown to allow enhanced lateral resolution in quantitative EFM and its application for dielectric constant measurement. Here we present the theoretical modelling required to quantitatively interpret the electrostatic force between these sharpened tips and samples. In contrast to a sphere-capped cone geometry used to describe metal/diamond-coated tips, modelling a sharpened silicon tip requires a geometry comprised of a cone with two different angles. Theoretical results are supported by experimental measurements of metallic substrates and ∼10 nm radius dielectric nanoparticles. This work is equally applicable to EFM and other electrical scanned probe techniques, where it allows quantifying electrical properties of nanomaterials and 3D nano-objects with higher resolution.