Ok, I found a Clarendon-like font online, Libre Clarendon.
Not sure whether to use the black, wide/normal etc. formats, as I’m not sure which one the original uses.
I’m not that much of a graphical designer myself (tho this task is not that hard), so I’m also not sure whether there’s a specific size the text should be, the ratio of the logo to the text, etc..
Perfect, the font you found looks really nice. Try a few different ideas for the “Powered by F” image and see. You can post your few best results and people can choose.
Even years later, I really like the Fortran logo. Great colors, great shapes. @jacobwilliams, @milancurcic well done. And perhaps most importantly, thank you the whole Fortran community for making this logo accepted everywhere as the Fortran logo. Huge achievement.
I thought, let’s give it also a try. I used DejaVu Sans Bold with tight spacing as a modern powerful tag to the classic Clarendon F logo and the frame line hints at an on toggle switch.
Nice, more readable.
Don’t know if this matters or not, but “Powered by F” might make it seem like we are referring to this: F (programming language) - Wikipedia
Fᴏʀᴛʀᴀɴ (small caps) was the original rendition, I believe.
The FortranFuture Network+ has a small amount of funding for what we’re calling ‘community assets’ (not for marketing campaigns) so if the fortran-lang community is so inclined, I might be able to arrange for someone to ‘polish’ a design, or small number of designs, that are proposed by the community.
I like this one. It does not create much empty space (by keeping the F smaller), but it does include the community logo. The hint at the toggle switch is a nice extra.
Indeed, it is small caps (Fᴏʀᴛʀᴀɴ) in the Programmer’s Reference Manual (October 15, 1956). But in the “Programmer’s primer for FORTRAN” (1957) it is FORTRAN in the text, but Fortran on the cover! 
It gets worse. People might think the language is F# or F* (or whatever programming language starts with F).
So, it might be better to have
<LOGO> Powered by Fortran`
or
<LOGO>
Powered by Fortran
or
Powered by <Fortran>
Where <Fortran> uses the same font as the logo.
I thought about the possible confusion with other (or subset) languages too. As for the design, another possibility might be something like “Powered by Fortran” where just the F in fortran is the purple background filled with white, and all the other letters have some consistent style and color (black over white, or purple over white, or black over transparent, and so on).
Perhaps something like this. It is very similar, leaves no ambiguity about the F, and still remains close to the F logo by using Clarendon, the same colour, and rounded corners.