Another trick in addition to the Randomized Response method whuber mentioned is a case where the respondent can effectively conceal sensitive information in the form of an aggregate response. The researcher can then back out some measures of the sensitive information across the whole population, but not at the individual level. I can't remember what this is called either, but here's how you would do it:
For example, say you were trying to measure the incidence of erectile dysfunction. This is something many people would be reluctant to admit and a yes/no question would be ineffective. You could randomly include/not include ED in a list of, say, 7 other ailments, some common, some uncommon. You could then ask a question like "Out of the following list of 7 ailments, how many have you personally experienced within the last 90 days?" Having kept track of the respondents who were given the list with/without ED, you might find that people listed on average 3.2 ailments in the ED-less list, and 3.7 ailments in the ED-containing list. This would give an expected incidence of 50%.
You can see that one of the drawbacks is the error. If everybody had ED then the mean would be expected to be 1 higher in the longer list, and if nobody had ED the means would be expected to be identical. So you are measuring a difference of two means on the range of 0 to 1, so it is necessary to have a large sample size, so the confidence interval for each mean is much smaller than 1.
It would be important to carefully select the other ailments - you would not want hardly anybody to need to give a "1" for only the sensitive response, because then it may not feel as concealed for the respondent, and similarly, you would not want anybody to need to give a "7".