In a sample of 2000 observations, no positive cases were found, but I want to still be able to provide an upper bound for the prevalence.

The general rule that people seem to use is to simply take 3/n, but this is the just same as the upper bound at 95% for 1 case found in the sample.

3/2000=0.15% and the upper bound at 95% for a prevalence of 1 in 2000 is 0.15%.

Surely if 0 cases are observed the upper bound should be lower than if 1 case was found? Are there any other methods I could use to keep in line with the upper bounds at a certain confidence level for other frequency results?