Unloading stiffness is a critical magnitude when extracting elastic modulus in instrumented indentation. Any phenomenon which interacts with its measurement may affect the final calculation of the modulus. Analytical and numerical calculations have been carried out to determine the influence of thermal drift and creep response on its measurement, and the predictions were in good agreement with experimental results. Since the influence of thermal drift is depth-dependent, it determines the effective resolution of an indentation device for a given material. In contrast, indentation creep significantly alters unloading stiffness even for weakly rate-sensitive materials (sensitivity exponent, m < 0.05) but its effect could be smoothed down due to measurement artefacts (unloading curve fitting strategy). For instance, for an ultra-fine grained (UFG) pure niobium at room temperature (m similar to 0.015 and H/E(r) similar to 0.02), the error in the measurement of elastic modulus with a typical nanoindentation procedure (5 s of holding time and 65 s of unloading time) can be as high as 15%. This paper proposes simple rules for a reliable experimental procedure to avoid both thermal drift and creep effects on the measurement of elastic modulus, which are especially relevant for the new generation of high temperature instrumented indentation facilities.