In the 1950's how were radio-astrometric positions with portable dishes so precise they could be assigned to their dim optical counterparts (Quasars)? In my question Why are quasars so far away that they couldn&#39;t be optically resolved in the 1950&#39;s? I included the following short paragraph, but then added strikethrough to the second sentence and added a parenthetical based on @DavidTonhofer's comment.

So today instead of &quot;quasi-stellar&quot; we might simply say &quot;unresolved&quot;. The light is star-like because the light from galaxies has a strong stellar component. (this second sentence is argued against in comments)

I then read further and found this short but informative historical account in University of Manchester's Jodrell Bank Centre for Astrophysics page The MKI and the discovery of Quasars:

Initially the radio sources were observed with the telescopes relativly close together. In this case the fringe pattern is very broad and greater than the typical angular size of radio sources so virtually all are observed to give fringes. However as the telescopes are moved apart, the fringe spaceing becomes finer and the fringes from many of the radio sources first reduced in amplitude and then disappeared. The separation of the telescopes when the fringes from each source reduced in amplitude (and the wavelength of the radio waves observed) allowed the angular size of the radio sources to be found.
To the surprise of the astronomers quite a number were found to have exceedingly small angular sizes - so small in fact that their images on a photographic plate would look like the images of stars. Much work then went into finding the precise location of these objects and finally it was possible to obtain their spectra. They were nothing like the spectra of stars or galaxies and remained a puzzle for some time. Finally it was realised that the reason that the spectra were so different was that the objects were so far away that their light was greatly red shifted. They were at very great distances away from us and so it was not surprising that their images were so small!
Because their images looked liked those of stars they were called Quasi-Stellar-Objects or QUASARS for short.

Question: In the late 1950's how were astrometric positions of these radio sources made so precisely that they could be assigned unambiguously to dim, star-like spots on photographic emulsions?


The 25ft Transportable Radio Telescope
In many cases in astronomy, there’s a difference in finding the position of something precisely vs. seeing detailed structure in that object.  In the former case, what you need to do is to find the centroid of the image.  So even with relatively coarse spatial resolution, you can often get very precise positions because you can centroid the images very well.  (EDIT: However, this may not apply to early radio observations because single-dish radio telescopes don’t form images.)
Specifically for 3C273, the first quasar identified, Wikipedia says that its position was refined with lunar occultation. This technique involves observing a source as the Moon approaches it and determining the precise moment when it disappears behind the edge of the Moon. Here you need to measure time precisely and to know the Moon's path very well.
Also see this answer to Has radio astronomy ever been done on objects that appear very close to the Moon? Is this avoided?
The first radio source to have a star-like optical counterpart associated with it was 3C84, and that was done by measuring the radio position precisely using interferometry, i.e. combining signals from multiple telescopes.
So I think that this was not in fact possible with single-dish radio telescopes in the 1950s, and required more advanced techniques that came a bit later.