Two things go wrong on cruises that sound similar and are not. The ship can miss a port, or the passenger can miss the ship. Policies treat them as unrelated.
A missed port is the operator's decision
Ports are skipped for weather, sea state at a tender anchorage, mechanical issues or a berth becoming unavailable, and the captain makes the call.
The passage contract almost always reserves the right to change the itinerary without compensation beyond refunding port fees and any excursion the line sold.
Insurance for this is a specific benefit that pays a modest fixed amount per missed port, and it exists because the contract gives so little.
A missed connection is the traveler's problem
Failing to reach the ship at embarkation, usually because of a delayed flight, leaves the passenger with a paid voyage they are not aboard.
Missed connection cover pays the cost of catching up with the ship at a later port, plus the unused portion of the cruise in some wordings.
It typically requires a minimum delay before it triggers, and the delay must arise from a listed cause rather than any reason at all.
Flight timing decides whether cover applies
Most policies require a reasonable connection time, and arriving on the morning of sailing may fall short of what the wording considers reasonable.
Flying in the day before removes most of the exposure and is the single most effective step, more so than any coverage upgrade.
Air booked through the cruise line adds the operator's own assistance, which is a separate protection from anything the insurer provides.
Interruption cover handles the middle of a voyage
Leaving a cruise partway through, whether for a medical reason or an emergency at home, falls under trip interruption rather than either of the other clauses.
This benefit covers the unused portion and the cost of getting home from wherever the ship happened to be, which can be substantial.
Medical evacuation is a further separate benefit again, and it is the one with the largest potential cost on an itinerary far from major hospitals.
Reading a policy against your itinerary
The useful exercise is to take the actual voyage and ask which clause would respond to each realistic failure, rather than reading the policy in the abstract.
Itineraries with many tender ports raise the missed port exposure, and remote itineraries raise the evacuation exposure, and no single limit covers both well.
Documentation requirements are the other thing to check in advance, since several benefits require evidence from the airline or the ship that is easier to obtain at the time than afterward.