Yes they do. In small countries the situation is even more personal and usually the PM himself is involved every time a citizen is caught behind enemy lines.
Happened quite a lot when the US started messing around with Gaddafi. Lots of Europeans working there were very reluctant to leave and then they returned there immediately after and had to be rescued again.
Do many small countries have the ability to project power like that in the first place? It's not the will to do it that is a problem - it's the infrastructure to generate a suitable force and put it on the ground that requires a very long tail of people, equipment and money on permanent standby, and of course you also need the expertise and experience to do it.
If you're a citizen of somewhere like Luxembourg they just don't have the capability to reach across the world into somewhere like Syria and rescue you like the US or UK would attempt to.
I believe most of these situations get resolved diplomatically. That doesn't work with IS, but the vast majority of cases are criminal rather than terrorists, or the result of general instability. A country like Luxembourg can usually find someone who has their money in their banks and is in a position to resolve the situation. There's also quite a lot of European solidarity in such cases.
Mass evacuations usually get several governments involved and they all contribute proportionally, or France sends a few planes and basks in the glory.
Regarding military operations to solve such situations it seems to me as if it's a matter not just of capability but of willingness as well. Europeans tend to think 50 cents to the foreign ministry is a better investment than $1 to the military, and that approach carries over in crisis. Empirically, my impression is that military action has about a 33/33/33% rate of success/dead hostages/"we just scared a grandma and couldn't find any hostages". Diplomacy has a higher success rate but it can take years. That's the sort of trade-off I don't envy politicians for.
Yes they do. In small countries the situation is even more personal and usually the PM himself is involved every time a citizen is caught behind enemy lines.
Happened quite a lot when the US started messing around with Gaddafi. Lots of Europeans working there were very reluctant to leave and then they returned there immediately after and had to be rescued again.