How to resupply ships that are sectors away?

1 hit resupply at nearest and the ship will limp back to the nearest planet
2 use an emergency resupply or reordinance pod which destroys it but gives you ship an amount of supply or ordinance hopefully enough to allow it to get back to a base quickly.
3 move a ship which is in supply out to intercept the ship which is out of supply and transfer supplies across

Techs which help with supply and ordinance also include result which upgrades planetary result depots. Cargo which makes supply and ordinance storage pods bigger and engines as higher tech engines contain a larger amount of supply than a lower tech one.

There are others but that will help

They have to be on the ship and I think they come up as an orders option if fitted not sure as I use the reserch cargo method to make sure my long range scouts have lots of resuply used to use them a lot in SEIV

You can also build a freighter and send it out to resupply the stranded ship.

use an emergency resupply pod on each ship and a repair ship-> unlimited supplies
a pod is only 10kt and a repair component lvl1(150kt) can repair 100kt/turn-> 10 pods turn...

"Can you expect the unexpected? No, you cannot. You can only expect to be surprised."

However you would need a repair frigate at least to carry the repair bay to go with the other ships so you would be talking about exploration fleets even if they where quite small say two scouts and a repair frigate

I assume you know about the stellar harnessing equipment (solar panels) you can fit onto your ship to generate supplies in systems with 1 or more suns.

I go for that tech right away.

In the stock game you have to research Astrophysics to get access to that tech. In the balance mod you get it right off the bat.

Used them a lot in IV and now on I use them on my covert scouts who end up spending a lot of time outside of friendly space and a long way from supply. However Astrophysics dose cost quite a bit if you start out as a young race that start of with a relatively small research base. Though as I have said elsewhere I don’t find it that hard to build a good research total, I even managed it when I got started in a system without any colonisable planets and one warp point on the other side of which was a xenophobic neutral race.

It was actually quite fun going to war in unshielded frigates with capital ship missiles and depleted uranium cannon