I seem to remember an article (maybe in the Legendariumcollection?) that discussed the possible 'historical' connection of Tolkien's certhas to the Germanic system(s). I don't remember the argument very well, but an overly strong connection is pretty hard to argue for, since for the most part there aren't even remote resemblances between Tolkienian and Germanic runes.
It's actually really hard to explain why the letters that were retained (the elder Futhark has only 24 runes, which is less than half the number of Cirth) would have such utterly reworked values (especially while keeping such remarkably similar shapes). For instance, Cirth #9 has the value /d/, but the rune of the same shape stands for /a/ - this is a truly drastic change! This sort of thing happens occasionally in the real world lives of scripts, but to get from the Certhas to the Futhark you'd have to imagine this sort of completely radical and bizarre shifting for virtually every letter.
Although neither statement was published, Tolkien does say as much in two writings connected to the drafting of the linguistic Appendices. These perhaps were removed partly because they were 'extraneous' enough when he needed to make the Appendices shorter, and partly because of how he ended up arranging the material in Appendices E and F (with most comments relating things to the modern day in F, but the scripts dealt with in E) - the point is, I don't think the fact that he left it out of the published Appendix means he necessarily rejected what he says. Anyway, early in the drafting Tolkien wrote thusly:
But whereas the flowing scripts (...) were developed in Elvenhome far from Middle-earth, the Runes, or cirth, were devised by the Elves of the woods; and from that origin derive their peculiar character, similar to the Runes of the North in our days, though their detail is different and it is very doubtful if there is any linealconnexion between the two alphabets. The Elvish cirthare in any case more elaborate and numerous and systematic.HoME XII: The Peoples of Middle-earth, The Appendix on Languages, p. 23
And a revision of this draft from later in the process:
...the Runes, or Cirthas they were called, were first devised by the Danians (far kin of the Noldor) in the woods of Beleriand, and were in the beginning used mainly for incising names and brief memorials upon wood, stone, or metal. From that beginning they derive their peculiar character, closely similar in many of their signs to the Runes of the North in our own times. But their detail arrangement, and uses were different, and there is, it seems, no connexion of descent between the Runes and the Cirth. Many things were forgotten and found again the ages of Middle-earth, and so it will be, doubtless, hereafter.HoME XII: The Peoples of Middle-earth, The Appendix on Languages, p. 75
In a way, I think this lack of connection is actually a good decision on Tolkien's part, since instead Tolkien designed Certhas as a plausible 'carved alphabet', meant to be chiselled on wood or stone, that followed principles of 'Elvish linguistics'. This means that, even though the Certhas had its origin in 19 'unsystematic' Cirth, the developed version we find in the Appendices very much resembles the Tengwar in principle, and even to a degree in shape.
Seen as a historical product within the early history of Middle-earth, it reflects the cultural milieu of ancient Beleriand very well: a rougher, 'organic' native culture (yet still one that invented writing on its own) brought into contact with and influenced by (though not replaced by) the very sophisticated Noldor with well developed intellectual traditions and an endless desire to know, identify, systematize.
It is laden with history, leading back into the dark heathen ages beyond the memory of song, but not beyond the reach of imagination.