For the eradication of an infectious agent, like bovine herpesvirus 1 (BHV-1), surveillance and certification can be used to reduce the transmission between herds. The goal of surveillance is that a certified herd that becomes infected is detected timely so that infection of several other certified herds is prevented. What counts is whether the reproduction ratio R, i.e. the average number of certified herds infected by one infected certified herd can be kept below 1. To support policy makers in making decisions about the minimal demands for a surveillance programme in an eradication campaign of BHV-1 in cattle, two mathematical models were investigated. With these models, the basic reproduction ratio between herds was calculated. The surveillance programmes were characterised with sample size, sampling frequency, test sensitivity, herd size, vaccination status, and contacts between herds. When R between herds is below 1, then the surveillance programme is sufficiently good to prevent spread of infection, provided that R is estimated well. In the model based on bulk milk testing sample size was replaced by a threshold at which bulk milk can be found positive. The R between herds was mainly influenced by the vaccination status, sampling frequency, and contacts between herds. Herd size moderately affected the outcome. Test sensitivity and sample size, however, were of minor importance. If herds of 50 cows became free of BHV-1 without vaccination, then spread of infection between herds might be prevented when animals within herds are sampled once a year (milk or blood samples). This frequency needs to be intensified, being twice a year, for larger herds and/or herds with extensive contacts with other herds. When bulk milk is sampled instead, sampling should be done at least every 5 months and more intensively, being each month, with larger herd sizes and more contacts between herds.