How would you handle a situation if you believed strongly in a recommendation you made in a meeting, but most of your co-workers shot it down?

Before or after the meeting explain the team to understand what and why is required, aand win the their support. 

I would put up an email to the team members explaining my point for two reasons:

• It offers an opportunity to relay my views without inference and also allows my team members time to read and digest and ensure they make informed decision. 
• It can be a lesson learned in future if I were to be right.

I would take a vote on it to see how many are for it and against it and then find out the reasons for them being against it.  If changes need to be made to the recommendation so that it would work better then I would go ahead and accept suggestions.

I would try my level best to get their confidence by letting them know the reasons and importance, pro's and con's of the proposed recommendation, also how  can we see or weigh the pro's and con's of the proposed recommendations and its effect on implementation. Thanks.

The reason is lack of Team Work. Before passing any recommendation, consult your team members or co-workers and take them into confidence and obtain their consent to it.