If I moved to the US part way through the year, how do I ensure the healthcare penalty is waived?

There is an exemption, however, I need a little more detail to give you a complete and accurate answer.  When did you move to the U.S.?  What is your residency status in the U.S?

Thanks for the response. I'm a British citizen. I moved to the U.S on 1st April, under a E-2 work visa

Were you able to obtain health insurance once you began to work?  The penalty can be waived for the first four months, but I want to see how to advise on the last 8 months.

I had healthcare from June to the end of 2017

Yes, you will be exempt.  For the months of Jan-April, you will be exempt based on you having been a nonresident for the period prior to your coming to the U.S. Here is how you will enter this into TurboTax:

1. Login to your account and click on Take me to my Return
2. Click on the Health Insurance section
   
3. When it asks you if everyone had health insurance, click no
4. Next click I'll tell you who had it and when.  You will select that you did not have insurance from January until May.
   
5. When you show that you did not have insurance from January to May, you will  you will select the penalty exemption of resident of another country.  You may see it in the screenshot below (within the blue box, 2nd option).  You could also claim the first exemption, lived outside the U.S. for 330 of 365 days.  (also in the blue box, 1st option).  Either of these options are valid in your case to exempt you.  May will also be automatically exempted as a short-gap exemption. (You will not need to enter anything into TurboTax for this exemption).

Here is the screenshot for this:  

Thanks for your help

You are welcome