Tip position modulation (TPM) involves moving the ultramicroelectrode (UME) tip of a scanning electrochemical microscope (SECM) perpendicular to the substrate in a sinusoidal fashion with a small amplitude compared to the tip/sample separation. The UME, which serves as the working electrode in a conventional voltammetric setup, is held at a potential to detect a species in solution at a transport-limited rate and the resulting current (ac and dc) is measured. This paper shows that tip-induced convection is an important factor in TPM. A model has been developed that describes the TPM response for the most challenging case of an inert substrate, where tip-induced convective effects compared to diffusion are greatest. The model provides an improved description of the ac response compared to existing treatment, as evidenced by the analysis of TPM-SECM approach curves (current-distance characteristics). The extension of the model to SECM-induced transfer is considered and it is shown that one can extract highly precise information on the permeability of a sample from such measurements, for which experiments and theory are compared. The prospects for using the technique more widely are highlighted and routes to improving the theoretical analysis further are briefly discussed.