(Not an answer, just an extended comment.)
I do not experience such problem with PDF files Export
ed by Mathematica 10.2 under Win7 x64 when opening them with Illustrator 17. The following is my check up.
Let us generate a Graphics
containing all the fonts available for Mathematica:
test = Graphics[{MapIndexed[
Text[Style[#, 10] -> Style["text", 20, FontFamily -> #1], #2] &,
Partition[FE`Evaluate[FEPrivate`GetPopupList["MenuListFonts"]][[;; , 1]], 47, 47,
1, {}], {2}]}, AspectRatio -> 1, ImageSize -> {Automatic, 800}]

We see that for some of the fonts the text string is not displayed inside of the FrontEnd. More informative graphics:
test = Graphics[{MapIndexed[
Text[Style[#, 10] -> Style["text", 20, FontFamily -> #1], #2] &,
Partition[FE`Evaluate[FEPrivate`GetPopupList["MenuListFonts"]][[;; , 1]], 47, 47,
1, {}], {2}]}, AspectRatio -> 1, ImageSize -> {Automatic, 800}]

From this we see that only "Euclid Math One" and "Euclid Math Two" are not displayed. Both these fonts contain no letters and are intended for displaying mathematical formulas, so we should not blame on this.
Export
ing:
Export["test.pdf", test]
Here is how exported PDF is rendered by Adobe Acrobat:

We see that some of the fonts are substituted, including "Euclid Math One" and "Euclid Math Two".
When I open this file with Illustrator 17 the following error window appear:

So "Fences" will be substituted. After pressing "OK" no other errors appear and here is how Illustrator renders the figure:

We see no boxes. The "Fences" font name is displayed as "Fences#20Plain* Regular*" but the actual displayed font seems to be "Times New Roman".
"Brush Script MT", "Bookshelf Symbol 7", "Fixedsys", "Euclid Symbol", "Euclid Math One", "Euclid Math Two", "Euclid Extra", "Mangal", "MT Extra", "MS Reference Specialty", "Harlow Solid Italic", "Script", "Roman", "Monotype Corsiva", "Modern", "Symbol", "Vivaldi", "Webdings", "Wingdings", "Wingdings 2", "Wingdings 3" and "ZWAdobeF" do present in the system but are substituted with "Tahoma".
"MS Serif" does present in the system but is substituted with "Times New Roman".
"Terminal" does present in the system but is substituted with "Courier New".
"MS Sans Serif", "Small Fonts" and "System" do present in the system but are substituted with "Arial".
The fonts "Arial Greek", "Arial Cyr", "Arial CYR", "Arial CE", "Arial Baltic", "Arabic Transparent", "Courier New TUR", "Courier New Greek", "Courier New Cyr", "Courier New CYR", "Courier New CE", "Courier New Baltic", "Marlett", "Times New Roman TUR", "Times New Roman Greek", "Times New Roman Cyr", Times New Roman CYR", "Times New Roman CE" and "Times New Roman Baltic" actually do not present in the system and are substituted with "Tahoma".
Other fonts seems to be recognized correctly. In some cases Illustrator displays the name of the font using Chinese characters, but for usual fonts it is OK.
First@ImportString[ExportString[Graphics[Text[Style["text",FontFamily->"Times"]]],"PDF"],"PDF"]
. It's not completely fool-proof with exotic Unicode characters, but usually gives me what I want. $\endgroup$TextMode
option in the linked answer is no longer needed to make it work (but doesn't hurt, either). $\endgroup$ImportString
approach is broken becauseImport
now can't importPDF
properly anymore. So maybe ghostscript as in one of the mentioned links would be a workaround. But it doesn't really answer your question, of course. $\endgroup$