The process I use for my websites, create a template with all the devices with masks for different screen sizes in photoshop or illustrator.
To get the website screenshots at the correct aspect ratio, I use firefox developer tools.
1)open the site in firefox,
2)right click anywhere, "inspect element"
then there is a button with an aspect ratio (highlighted in screenshot) click that and you can select different device widths, for a screenshot, click the camera and you get the screen without the tags.