I found that https://wordpress.org/plugins/pinterest-widgets actually has the needed functionality but doesn’t mention it in the description.
After installing and activating you can add a pinboard to a post by using the following shortcodes
[pin_board url="http://www.pinterest.com/pinterest/pin-pets/"]
[pin_board url="http://www.pinterest.com/pinterest/pin-pets/" size="header"]
[pin_board url="http://www.pinterest.com/pinterest/pin-pets/" size="custom" image_width="100" board_width="900" board_height="450"]
more options can be found on the plugins “settings” page after installing.