How to get HTTPS on Arduino?

MCUs mounted on Arduinos don't have the horse power to handle https connections.

Yún does handle https on the linux side, with software like curl, wget or python. Your sketch can just delegate the task to the linux side.

While curl works fine, despite having python preinstalled, you need to manually install python-openssl, since it's not available out of the box (due to disk space constraints)

^{(Disclaimer: I'm actually the author of the evothings.com article)}
The Arduino UNO is more than capable at doing TLS. I've just finished up a blog post series on the topic. I have a working example of an Arduino UNO doing elliptic curve cryptography (sect163r2) to exchange an AES-128 key for continued communication.

http://ardiri.com/blog/utls_defining_lightweight_security_for_iot_part_1
...
http://ardiri.com/blog/utls_defining_lightweight_security_for_iot_part_8

I took an alternative approach to trying to make a true HTTPS connection - instead, this is using the same protocols under the hood but using an insecure communication channel to do so. Pretty much TLS on HTTP.

I don't think it is possible due to the size and complexity of the SSL Library, because the Arduino would most likely be under powered. That being said you could make the requests to a regular server and use some sort of PHP script to proxy the request to the HTTPS server. Not sure how well it would work though.

You may be interested into looking at this.