How do you ensure that remote team members feel as engaged and included as those who are in the office?

I think you need to have both regular one-on-ones with them so they can speak frankly and freely, but also have regular “all hands” and town halls so they can engage with the team overall.

Encourage them to turn on their camera on all meetings, not to monitor them, but so they get full engagement out of their time on meetings. I was based in TN and my entire team was in WA and I knew them like they were in the same room because they were on my camera all the time. 

Good previous comments!  Understanding why someone is remote is helpful.  

If they're the lone person in their country for example, then having a deliberate buddy at the office to keep them involved works well.  Someone who is good at being a buddy, not just someone who does the same job as them.

If they can, then I do think it's important they spend some time physically connecting to their in-office colleagues - so creating moments where that happens is important - moments where good work is done, but a social element is built in.  And it works both ways, they also need to make sure they are engaged and include themselves.

Don't stop there...  Ask, How might we make remote work even more engaging and interesting as in the office?  Humans push boundaries we don't strive to just copy what already exists.  

Imagine if you have a workplace with no space constraints, no travel time, and no limitations on the wisdom that any one in the organization can offer. that is a remote organization.    

The use of digital techology like slack and MS teams to enable asynchrounous work and reimagine workflows, how information is shared, how people collaborate and even 'who's in charge' is a real opportunity. 
- Remote work is still the same humans who crave mastery, autonomy, purpose, growth, connection meaning, etc.   A shift to remote work can be a reason to lean into these drives with personally accountable, mission aligned teams, dedicated learning and teaching space, as well as intentional methods to connect as interesting and flawed human beings.    
- Virtual tools like Mural and Miro enable a far greater amount of participation and transparency in real important conversations like strategy and such.  Transparency, bringing the wisdom of all, and more opportunities for seamless co-creation and collabroation exist.  

I think intentionality is key. It's easy to let "out of sight, out of mind" take over. Make time on your calendar to engage with the remote team members.