The best way to convert a high-definition signal like HDMI into coax is to use an HDMI-Over-Coaxial converter. These will typically be able to convert the HDMI signal so that it can be transmitted over coaxial cable or vice versa.
It is helpful to know that while a high-definition signal can move along a coaxial cable, there is likely going to be some degradation to the quality of the video feed, meaning it may not have the same resolution as the original HDMI. Conversely, converting a signal from the coaxial cable to HDMI will not transform it into high-definition if it did not originate that way.
HDMI-Over-Coaxial converters vary in price from approximately $20 to over $100, depending on their quality and other features. The more expensive adapters will render higher quality pictures and retain more of the high definition inherent in the HDMI cable. Using high-quality or professional grade coaxial cable can also improve the picture resolution since there will be less signal degradation as the signal travels along the cable.
It is also possible to use a cable or satellite box to change an HDMI signal to coaxial cable since many of the newer models carry input and output ports for both. These are often preferable to using a third-party adapter since it will work in direct conjunction with a cable or satellite provider.