Last week saw GM Jon's ongoing voyage of the Modiphius Star Trek playtest and in this particularly suspenseful episode, the crew had lost power to their ship whilst drifting slowly towards the Klingon Neutral zone. If I remember the after drinking conversation, and I don't particularly, the power outage was caused by an encounter with or proximity to a spacial anomaly - wormhole possibly.
Now Starfleet ships are not cheap bits of kit I would imagine but I would hope that there is a manual or possibly pdf available to the occupants and I would hope that there are some guidelines regarding power loss. If it were me of course I'd try the obvious, like turn it off and back on again or raise a call to the Starfleet help line, though I would suspect it would all be outsourced to native Ferenghi call centers - I don't recall any tense moments in the original series where Scotty was drifting towards oblivion whilst being on the communicator listening to the Coldplay on hold music - not a nice way to go. I'd imagine with a lot of intrepid vessels in various situations at any given moment in time that it would mean enough staffing in the galactic customer service centers and hopefully the call will indeed be important to them when the time comes.
As I understand it the crew did in fact manage to get the power back up in time and as it happens the drifting did buy them enough time to probe the structure of a Klingon ship lying in wait for them and expose enough tactical weaknesses to have the upper hand in combat. Though I am sure there are political ramifications, the nature of Neutral zones make no mans land a bit of a free for all if any Captains need to blow off steam.
I do like the heavily compromised vision of the Star Trek future beneath the veneer and it does remind me of the numerous neutral areas still in play on our own planet, principally the North/South Korean divide comes to mind but interestingly DMZs also include Antarctica, Sinai, Svalbard and the Aegean Islands so I would recommend taking something resilient on a typical 18-30 caliber holiday if you fancy a Spring break in Greece.