Standard errors for part-worth utilities are certainly related to standard errors from simulations, but there isn't a mathmatical way to relate one directly to the other. Has to be done empirically once the data have been collected.
Simulations are done (share of preference case) by summing up the part-worths, then taking their antilog, and then percenting the results across product alternatives to sum to 100%.
The easiest way to explain to less-technical clients is to give the margins of error based on the rule of proportions. In other words, 1000 respondents gives you roughly (worst-case scenario) +/- 3% margin of error in market simulations.
This is the conservative way to explain things to the client, though you'll get better than +/-3 3% margin of error with 1000 respondents due to:
1. +/- 3% is based on the worst-case scenario of 50% share of preference...and your shares of preference are unlikely to be around 50%.
2. You actually get more statistical information from each respondent than a simple "first choice vote" since the probabilities of choice are split in a continuous fashion among alternatives.
The simulator reports the actual margin of error based on the respondent data and the share of preference rule (or RFC, which also gives you continuous probabilities of choice). You can use data from a previous similar project to estimate approximate margin of error for your next project.