What are the best secure browsers for iMac running High Sierra?

Firefox ESR (Extended Support Release) is still current on Sierra, High Sierra & Mojave and will continue to be updated until at least August 2025.

Can I still browse safely with Firefox macOS 10.12, 10.13 or 10.14?

Mozilla is providing critical security updates through the Firefox ESR channel up until the end of ESR version 115, August 2025. After this, no security updates will be provided and you are strongly encouraged to move to a supported version of macOS. (see https://support.mozilla.org/en-US/kb/firefox-users-macos-1012-1013-1014-moving-to-extended-support)

You can dowload Firefox ESR here -> https://www.mozilla.org/en-US/firefox/all/desktop-esr/

You’re not likely to find anything that will work. High Sierra is way too old.

3rd party developers have largely stopped supporting it.

Apple stopped supporting it almost 5 years ago.

You’re going to need a newer Mac. That machine is long obsolete.

MartinR wrote:

Firefox ESR (Extended Support Release) is still current on Sierra, High Sierra & Mojave and will continue to be updated until at least August 2025.

Looks like Mozilla extended the deadline again.

First Mozilla was going to stop providing critical security updates as of September or October 2024. Then they pushed back the date to March 2025. Now it's August 2025.