Think of Venue
If you do not have details, even name of the person, let alone the contact details, you may think of venue you met the person. In case, you had met that person at a seminar or conference, you might be able to get contact details from the organizers, as it is possible that the person had left contact details with them.
Think of Obvious Features
You may also think of obvious features of the person and ask from people who might know that person. Particularly, if you have met that person at a conference or any social gathering, you might be able to find their contact details.
Search on Social Networks
If you know some details of the person, you can try your luck and search online, either Google it or search on the social networks such as Facebook.
Post as much details as you know about the person and request for meeting again. Also, leave your contact details with a general message that if anyone knows of the person you are looking for, let you know. It is possible that you get yourself informed by someone who holds some information.
If you hold some information or routine details of the person, you can follow that routine for a few times. For example, if you met the person at a bus stop, it is possible that the person takes a particular route bus on a daily basis to office or any other place. Note down the time and date and the day you met the person, and try to be there at the same time, date and day for a few times. It is possible you find that person in the same routine.
It is possible that you meet the person you are desperate to meet by sheer amount of luck. So while thinking or missing the person badly, be patient and you might be able to meet by chance. After all, there is nothing much you can do.