A common statistical problem is to make inference about the mean of a normally distributed population. While the mean and the variance are important quantities, many real problems require information on certain quantiles of the population which combine both the mean and variance. Motivated by two recent applications, we consider simultaneous inference for more than one quantile of interest. In this paper, a set of exact level simultaneous confidence intervals for several quantiles of a normally distributed population is constructed, based on a simple random sample from that population. The critical constants for achieving an exact simultaneous coverage probability can be computed efficiently using numerical quadrature involving only a one-dimensional integral combined with standard search algorithms. The proposed methods are illustrated with an example. Several further research problems are identified.