I understand getting stuck with a less-optimal solution because of choices made elsewhere. About all you can do it inform the client of the ramifications of their decision and prepare.

In the first case I would handle it like this. Tell the client company:

Since your current webhost doesn't support A, B, or C we can develop your project in X weeks and it will take about Y effort to support in the future. It will scale like Z. If you find a webhost that supports A, B, and C then we can implement it in T weeks and it will take about U effort to support in the future and it will scale like V.

Break it down in such a way that both their operations staff and accounting departments can both understand the ramifications of the choice they've made. If they choose to stay, at least they know what tradeoff they made (and hopefully they'll come back to you when they realize the error of their ways). Also, if you can get your company to change policies and start recomending a (or some) particular webhost(s), you may be able to cut a deal w/ the webhost that would let the clients get a lower rate (since you'd be bringing them in in bulk).

In the second case (and I've been in that EXACT same spot before w/ HP-UX and Oracle even). be sure you include in your specifications details requirements of what they must have installed (preferably in an early spec that upper-managemet signed-off on). Make sure this is widely distributed to all parties related to your project in the client company. Make sure you are ready so if it comes down to the dinosaur manager problem you can place blame squarely on his/her shoulders and show him/her that upper management has already signed-off on it. It still isn't a fun fight to have, but being prepared can make it an easier win.