Providing certain assumptions are made, the standard error of the median can be estimated by multiplying the standard error of the mean by a constant:
Algebraically speaking 
SE (median) = 1.2533 × SE()
where:
 SE (median) is the standard error of the median,
 SE () is the standard error of the mean.

The assumptions are:
 the sample size is large
 the sample is drawn from a normally distributed population
Since the median is usually only used when the data are not drawn from a normally distributed population, this rather limits the usefulness of this formula, and it is rarely used.
A better approach is to use simulation.
For example, using R, it is simple enough to calculate the mean and median of 1000 observations selected at random from a normal population (μ_{x}=0.1 & σ_{x}=10). Repeating this calculation 5000 times, we found the standard deviation of their 5000 medians (0.40645) was 1.25404 times the standard deviation of their means.  In good agreement with both the (approximate) formula above  and with the estimated standard error for such a mean (using σ_{x}/√n).
Following an identical procedure, sampling a slightly skewed population, the standard deviation of their medians was only 1.19698 times the standard deviation  and when we sampled a highly skewed population, the standard deviation of their medians dropped to just ^{1}/_{10}18 of the standard deviation of their means.