I agree that UA.com is good for routine economy class awards to Europe. If you check the box for flexible dates and award travel, you'll get a calendar for the month of your departure that's color-coded to show what days have saver availability. All you have to do is pick a day of the month and a list of possible routings is presented showing which have saver availability. Do the same for the return and you've got the info you need when you talk to US res agents.
Before UA & CO merged res systems, I used the CO site to pick dates and routings for a trip my wife is taking (originally to Basel, Switzerland). US's site didn't know that Basel existed, UA's site recognized it but showed no availability, but CO's site gave numerous routings with availability each way each day. The CO site is now the UA site.
Jim