We explore the use of magnetic resonance imaging (MRI) velocimetry and pulsed field gradient nuclear magnetic resonance (PFG NMR) data for studying the flow characteristics of yield stress fluids through model pores (a succession of ducts of different diameters) or real porous media (bead packings). We propose different methods for the quantitative analysis of the velocity field, aimed at getting a deep understanding of the different flow regimes (solid and liquid) which typically take place in such fluids and at seeing how the transition from one to the other occurs in space or in time. Our approach exemplifies interdependences between PFG NMR data and local flow features and how the statistical velocity distribution function obtained by this way can be used and/or processed for extracting quantitative information concerning critical flow characteristics at a local scale. This provides a solid framework of analysis of flows through porous media with pores much smaller than the resolution of MR velocimetry.