Yes, I've rooted a sambac jasmine in plain tap water. The cutting I took was about 3-6 month old. Took about 2-3 months to root.

Other ways would be to root it directly in soil with some rooting hormone and tenting. I used "water in a glass" method so I could see what was going on with the cutting, but others have had success with the soil method too.

There are several posts regarding this information - in detail "how-tos", if you search for it, you'll find them!

Good luck with your cuttings.

Thank you, Mams...for letting me know...where are you from? I'm also rooting it in water...but it's rain water with a pinch of epsom salts and a few drops of Schultz's micro nutrients, how easy or difficult to "find" the "Grand Duke" Jasmine??? Now I've added Jasmines to my fragrant outdoor plants. I'm growing Plumerias with quite some success!!!!
Annamaria

My most favorite rooting method is called the Forsythe Pot. It's so easy!!! Take a look:

http://www.extension.umn.edu/distribution/horticulture/DG4419.html

I'm sure you'll find grand dukes in local nurseries as the weather gets warmer. I did see it at HD last year, but did not buy it since I thot it would be a finicky plant to care for.
I am located in the SJ-Bay area, and these last couple of summers have been mild at best. Even my sambac jasmines have been struggling to catch up and grow beyond the previous year's growth!! Even with all the help I can give them..
Anyway, I really hope that your plants do much better than mine - these microclimates are very different from one place to other, and if you've been having success with your plumerias - thats amazing.

Annamaria
If you really want some good Duke of Tuscany Jasmin. Almost Eden is the king of Jasmin. Those people are so professional they restored my faith again in the on-line nurseries. I used several On-line Nurseries and I can write a book about my disappointments. But not Almost Eden. You get exactly what they say you will get, plants are very healthy and the way they ship them is amazing. They shipped my plants in a separate tubes and the pots are rapped in wet paper towels. The Shipping did not cause any shocks. I hope you don't think I am a salesman for them I don't even know where they are may be somewhere in the south west.
As for propagation I do it for all trees. I use the air layering for big trees (very easy and sure way. and I use the baggy method for small trees. You put the cutting into a plastic bag filled with wet sphagnum moss. In summer keep the bag in your car to take advantage of the solar energy, in winter I put it on a heating mat. The Cup and water way works too but from the research I read the roots are weak, short and lazy. Under the theory if water is plenty and available why grow and run to find water. I don't know I am not an expert I just read a lot.

Thank you,"foolishpleasure", I like your way...does it have to be a "thick" stem to be successful? How big was the Jasmine you ordered? I'll check their website.
Thanks again for your help,
Annamaria

Thank you "foolishpleasure", how thick or long does the cutting need to be? Where are you from?
Thank you, again,
Annamaria