Specifically, I'm curious about situations where it's not immediately apparent that it'll be necessary. For example: you don't know whether or not you'll need an epipen when you leave the house, but could you carry one with you anyway?
My rabbi told me that I should carry candy with me everywhere I go on Shabbos, out of concern for hypoglycemia, which is a life-threatening condition. Hypoglycemia (also called "low blood sugar," or just a "low") is a function of type 1 diabetes. A low can come almost without warning, even with the best control (trust me, I know).
If I'm going long-distance, I'll also carry a blood glucose meter and some other stuff I might need.
Where there is no eiruv, I carry whatever I need with a shinuy; socks are useful, and should work for an Epipen also. As Avrohom Yitzchok already pointed out, arranging to have what you need wherever you go is a much better idea, provided you have enough medical devices to go around.
(I have, at times, placed up to four meters in different buildings around a city I visited on Shabbos that didn't have an eiruv)