Do you have FMP10?
Define your drop down field as a global field.
If you use FMP 10, Define a script trigger for the field to perform a script similar to this:
Enter find mode 
Set Field [YourTable:: ProjectIDField; YourTable::globaldropdownfield ]
Set error capture [on]
Set error capture [off]
//you can do other steps here like sorting your records or popping up a message if no records were found.
If you don't use FMP 10, then place a button next to the menu and set it to perform this script.
Which script trigger should you use? Well that can depend on your preferences and what type of menu (Pop-up or drop down) you select.
I use "On Modify" with pop-ups and "on Exit" with drop downs usually.
Well, this must be some kind of record. I came to this forum to get exactly this answer, and found it in less than a minute!
BTW, it appears you need to add the little button next to the drop-down or pop-up to run the script if you are preparing the layout for web access.