edit: For the purposes of this exercise, one could consider using three or four identical spacecraft, and using the "best two out of three (or four)" for interferometry at any given moment.
In 1994, STS-59 and STS-68 flew Spaceborne Imaging Radar, a type of Synthetic Aperture Radar (SAR). SAR is a type of interferometric radar where phase information (relative to the onboard local oscillator) is recorded and the interference phenomena is calculated/simulated offline during analysis. Instead of multiple antennas, multiple data sets are recorded with the shuttle or spacecraft in different but nearby positions in its orbit.
Two sequential measurements milliseconds apart provides the separation in the orbital track direction, but near-coincidental ground-track orbits separated by long periods of time are necessary to get displacements in the perpendicular direction.
So in 2000 STS-99 was launched with the Shuttle Radar Topography Mission. By extending a second antenna 60 meters away from the shuttle perpendicular to the orbit track, interference in this direction could be implemented with conventional interferometry, while the SAR-like data analysis was still used for the orbit direction. below: from here.
Without the mechanical extension, if the 2nd antenna was at the same altitude as the shuttle and moving parallel, it would collide with the shuttle in one quarter of an orbit. This is because their orbital planes would intersect. Conventional parallel orbits around a spherically symmetric body do not exist. (Let's leave discussion of exotic orbits around cigar-shaped bodies to other questions.)
As an exercise, what kinds of orbital solutions exist if the extension scaffolding were not used? Suppose it wiggled too much for a hypothetical next generation shorter wavelength system, or that a longer baseline was desired. Suppose also you could use more than one antenna.
Question: What orbital "tricks" could be used to provide at least one antenna orbiting roughly parallel to a primary spacecraft at any time? The separation does not have to be constant, it just needs to be known/predictable, and should keep working for a few weeks at least.
note: Now that we have independently flying antennas, an additional unit could fly ahead of the primary without problem. That may or may not eliminate the need for SAR analysis, there may be other benefits such as the much large effective baselines. Also, assume optical links between spacecraft, so no more coaxial cables.
below: "Space Shuttle Radar Topography Mission Canister, Antenna" from the Smithsonian National Air and Space Museum A20040261000d20.