The jet opening angle and inclination of GW170817 - the first detected binary neutron star merger - were vital to understand its energetics, relation to short gamma-ray bursts, and refinement of the standard siren-based determination of the Hubble constant, H-0. These basic quantities were determined through a combination of the radio light curve and Very Long Baseline Interferometry (VLBI) measurements of proper motion. In this paper, we discuss and quantify the prospects for the use of radio VLBI observations and observations of scintillation-induced variability to measure the source size and proper motion of merger afterglows, and thereby infer properties of the merger including inclination angle, opening angle, and energetics. We show that these techniques are complementary as they probe different parts of the circum-merger density/inclination angle parameter space and different periods of the temporal evolution of the afterglow. We also find that while VLBI observations will be limited to the very closest events it will be possible to detect scintillation for a large fraction of events beyond the range of current gravitational wave detectors. Scintillation will also be detectable with next-generation telescopes such as the Square Kilometre Array, 2000 antenna Deep Synoptic Array, and the next-generation Very Large Array, for a large fraction of events detected with third-generation gravitational wave detectors. Finally, we discuss prospects for the measurement of the H-0 with VLBI observations of neutron star mergers and compare this technique to other standard siren methods.