Another inane question from yours truly. Ok, so whereabouts is the longest stretch of coast between two ports, south of the Arctic Circle?
In other words where lies the longest stretch of coast that doesn’t have a port?
How large does the port have to be to qualify?
My WAG is Antarctica.
I hadn’t considered Antarctica, I suspect you’re right. Other than Antarctica then, places where people actually tend to live where would it be?
How are you defining length of coastline? It’s a nontrivial question.
The distance between one port and the next port down on the same landmass.
This isn’t something I had considered, maybe I should limit the question to cargo ports?
I don’t think there’s any kind of port between Huonville and Strahan in southwestern Tasmania, because the area between them is pretty well uninhabited. Similarly, there would be no port between Esperance, Western Australia, and Ceduna, South Australia. Google Maps gives the road distance between Esperance and Ceduna as 1,400 km, which would seem to be a hard distance to beat.
As the crow flies? Or following the coast? Because then you have to define how granular a deformation of the coast has to be, because otherwise every nook and cranny in an undulating coastline would be counted, whereas if you are allowed to smooth things off a bit, so to speak, the apparent coastline distance will be a lot less.
Technically you don’t have to define the length of the coastline, only the partial ordering relation “is longer than” between two segments of coastline.
For example, for two coastline segments, A and B, and a distance delta, define:
A is_longer_than[delta] B if the piecewise linear approximation of A with segments of length delta is longer than (by the conventional definition) the same approximation of B.
Define the delta-independent relation is_longer_than by:
A is_longer_than B iff there exists some D such that A is_longer_than[delta] B for all delta < D.
Then you can partial order any set of coastline segments without defining a length, and hope there exists one element that is_longer_than all the others.
Arguably, that might be a bit pedantic, though. 
I think the best way of defining distances between ports is the shortest way to travel between them by ship (including travel via canals, if that’s available).
This. Giles’ 1400Km gap sounds to me hard to beat but perhaps Chile, Alaska, or Canada can beat it? Maybe somewhere in the Russia Far East too?
If you add canals, do Africa and Asia still contain a coastline? The Panama canal is a bit different because it’s a canal system with locks and a lake in the middle. I don’t know if this affects the outcome in anyway. Although I do find some goalpost creep since the OP
(An Gadaí - I was pretty sure you had forgotten about Antarctica, but its a good goto continent for geographical trivia)
I think that Walvis Bay, Namibia and Luderitz, Namibia (on the South Atlantic) are that country’s only ports, so there would be a long stretch of port-less coastline between them, and to the north of Walvis Bay.
This site may help:
Churchill, Manitoba is a seaport on Hudson Bay. It’s well south of the Arctic Circle, although the climate is definitely arctic in nature. I’m not sure what the next seaport is in either direction, although the one to the west is above the Arctic Circle. Barrow, Alaska would count, but I think there may be a port on the north coast of Yukon Territory or NWT which would be closer.
To the east, the next port is probably Goose Bay in Labrador. It’s well more than 1400 Km between those two ports directly and way, way more than that along the coast. At a guess, it’s probably over 5000 Km. That coast between them is all below the Arctic Circle. Unless there’s a port between those two, that’s probably the answer.
No ports in Northern Quebec?
How many ports are on the Kamchatka Peninsula?
Here’s something you can use to investigate - an interactive map of port locations:
ETA:
Didn’t see it was already posted - sorry.
Checking the site provided by spikebrennan, it looks like the next one to the east is Sheshatshit (gawd, what a name!) Harbor, which is a short ways away from Goose Bay. So it’s almost the same distance.
Have no idea what the distance to travel between them by ship is, although it’s considerably less than the coastline. Still would beat the 1400 Km.
I don’t think there’s anything in Russia below the Arctic Circle that beats it so I reckon we have a winner with the Canadian entry. Thanks everyone for your input.
Using the linked website, the longest stretch along the Kamchatka Peninsula without a port appears to be from Ust Kamchatsky to Beringovsky, which looks to be about 750 miles as the crow flies. The coastline between Petropavlovsk-Kamchatsky and Madagan is a good deal longer, but most of it is a long bay off the Sea of Ohkotsk, along the western coast of the peninsula (does that bay have a name?); the sailing distance is probably less.
ETA: Ah, it’s the Shelikhov Gulf.