I've been on both sides of it - more than once pulling out all the stops to get someone home and then as the passenger desperate to get to the other end.
As a crew, requesting short-cut after short-cut to get someone home, we were once cleared direct across France from one FIR boundary to the other while the French ATCers moved everyone else out of our way. The airfield nearest to where our passenger was going in UK stayed open just for us. I doubt he ever knew the efforts that had been made to get him home as fast as possible, he had other things on his mind.
On the other side I was on Op in Thumrait when I received a 'call' from home. The in-theatre 125 stood-to, started as soon as I stepped on board, took me to Muscat where a chap from the Embassy walked me through the departure procedure (I had no entry visa from the civvie side) until I went through into departures and joined a BA flight to Heathrow. At the other end a driver from home-base met me and asked if I'd like to go to the base and collect my car or straight home. I went straight home. After receiving the call at 4pm UK time in Thumrait I walked into my living room at 6.30am the next morning. I cannot express how grateful I still am for the 'service'.
From both sides, we do the comp case very well. The reassurance that gives when serving away from home is immeasurable.