Give me the estimate

If you are managing people who are doing work that has not been your forte then estimation can be deluding process for you. You can't estimate yourself in this case so first you ask for estimates and then try to validate them. The moment you ask for estimate from a person you are asking for his commitment, asking for his word. No one in this world wants to be proven wrong, even to himself. No one wants to go back on their words. So the moment estimate is asked that person start to estimate by including all risks, all possible disasters that may happen, all possible subjective worries. When estimate is done after factoring in all these fears no doubt estimate will be inflated. 

You can get estimates reviewed by peers or specialist within/outside team but most probably you won't find any deviation. People within an organization have a healthy fear or healthy respect or social/professional dependency with each other so until something is not glaringly wrong it won’t be pointed out.
Validating estimate by established estimation standards never work. Standards are too general whereas estimate has to be specific. So standards can act as guideline but they can never validate estimate.
Getting estimate from a person and then boss him to cut it down 20% and then continuously sit on the top of his head to finish it even faster never helps.

So how work can be get done in more efficient manner?  

By placing your faith in the person. Tell him not to worry about missing deadlines, not to worry about repercussions, not to worry at all. Request him to work, just work and give his best. By faith all the buffer estimates (read fears) evaporates. Once the assurance is given to the person, keep faith in him. Don’t start moaning the moment something goes out of the line. Keeping faith doesn't mean that you forget about him. Do keep track of the progress at mutually comfortable level. Keep judging the person. If at any point you feel your faith is being misused, act.

There are circumstances when estimation will be mandatorily required so only faith won't serve the need. But whenever possible give faith a chance.

Faith will give you positive surprises. In today’s world people are not treated with faith and that’s why world is so cynical, cautious and inefficient. You give a person your faith and there will be occasions when you will be pleasantly surprised. There will be times when you’ll find gem of a person.