I've found the best estimates are not estimates but non negotiable deadlines with fixed outcome.
"You have six weeks to do X for $$$" or "I'll get it done in six weeks or you don't pay"
Where i work there is no penalty for being late or not hitting a deadline. Life goes on and work continues. I have seen when there are specific dates and metrics and suddenly people work in focused effort and sometimes work weekends or celebrate with finishing early.