Do you work well under pressure? 

The interviewer wants to know how you will deal in stressful situations by asking this question.

Sample answer:

I react to situations rather than being stressful. I want to make the situations not to be stress for anybody. If a situation seems overwhelming, I mentally break it up into smaller steps and just focus on reaching each one on the way to accomplishing the larger task. Once I had a situation that in the same week i had to submit two projects which is very pressure to me. As i was skilled in multiple tasks, i just break down all the works i have in to smaller assignments and just worked one by one to complete the whole task. By this way i handled my stressful situation and submitted my projects within the due time.

Ofcourse, such situations helps me to stay motivated and productive.

Tell us about a time when you missed a deadline.

(or)

Let's discuss a time when you missed a significant deadline.

If you answer something like "You never missed a deadline". Most interviewers will immediately conclude you are not experienced and may also feel you are lying. 

Approach - It is absolutely necessary to accept that you have missed a deadline and give reasons how you resolved and what you learned from it. This will demonstrate your experience.

You could say in one of the first projects earlier in your career you missed an important deadline and made the boss very upset. It was a great learning experience and after doing some introspection, you realized, you could have done better planning, prioritization and communication. Now, you use special tools, processes and methods to address these issues. Now your team, colleagues and management are always up to date so no surprises arise on meeting deadlines. 

Below are few things you may emphasize on in your response...

Effective planning

Procedural Improvements

Better Prioritization

Open communication

Better Status reporting

How do you handle stress?

Wrong approach -
Do not say you are never under stress or I hate stress or you do exercise and meditation to take care of stress. Focus strictly on professional things that you do.

Right approach -
A good response is to say that pressure helps you focus and maintain your drive and like to handle challenges. Explain that some of your best efforts are the result of stress and pressure. Also inform that when pressure gets too intense, you know how to handle it.

Example -
Stress and pressure are a challenging part of the job and i know how to handle it. I handle it by focusing on proper planning and reporting, better time management, open communication, Hard work and prioritization.