Q:

Do wifi and cellphones increase the risk of miscarriage?

Over the past few days, a whole bunch of news articles have claimed that WiFi and cellphone signals increase a pregnant woman's miscarriage risk. Some examples:

"WiFi and mobile phones could increase pregnant women's risk of miscarriage, study claims", The Mirror (2017-12-15):

Results reveal pregnant women with the highest MF-radiation exposure have a 48 percent greater risk of miscarrying than those with the lowest exposure.

"Wi-fi and cellphones increase pregnant women's risk of a miscarriage by nearly 50%, study reveals", Daily Mail (2017-12-14):

Magnetic field (MF) non-ionizing radiation is also given off by power lines
Pregnant women exposed to the highest levels are 48% more likely to miscarry
Some 24.2% of such women miscarry versus 10.4% with the lowest exposure
MF radiation, which everyone is exposed to, has previously been linked to cancer
Miscarriages affect between 15 and 20 percent of pregnancies in the US 

"Wifi signals and mobile phones ‘increase your risk of miscarriage by a THIRD’, experts warn", The Sun (2017-12-14):

The women were asked to disclose if they had previously had a miscarriage, smoked, drank alcohol and had suffered any fever or infection - all factors that can increase the risk of miscarriage.
Of the 913 women who participated, those who were exposed to the lowest amount of radiation were 10.4 per cent more likely to suffer a miscarriage.
Women who were exposed to higher levels were 24.2 per cent more likely to have a miscarriage.

All of these articles claim research done by the Kaiser Permanente Division of Research in Oakland, California, and published in the journal Scientific Reports.
I have tried my best to track down the paper in question to establish if it really has some actual basis. Additionally, I have tried to find out if this research company and the journal they published in are reputable. I haven't had much success. 
Do these claims have any proper, reputable basis?

A:

No, wifi and cellphone radiation have not been shown to increase the risk of miscarriage.
A recent peer-reviewed publication suggests a correlation between magnetic field exposure from all sources and miscarriages, but correlation does not imply causation and the frequencies tested are far smaller (40–1000 Hz) than wifi/cellphone EM frequencies (800–2600 MHz).  The publication does not suggest any possible physical mechanism to explain the correlation and thus does not establish causation.  The paper does not claim the correlation is specifically due to magnetic fields from wifi or cellphones.  There are some other weaknesses in the study that are not addressed, such as an explicit discussion of the frequency of the fields.  From the testing device used, this appears to be in the 40 Hz–1 Khz range, far below wifi/cellphone radiation and rather in the range of alternating current power.
The original publication is:
De-Kun Li, Hong Chen, Jeannette R. Ferber, Roxana Odouli & Charles Quesenberry.  Exposure to Magnetic Field Non-Ionizing Radiation and the Risk of Miscarriage: A Prospective Cohort Study.  In: Scientific Reports 7, Article number: 17541 (2017), doi:10.1038/s41598-017-16623-8. https://www.nature.com/articles/s41598-017-16623-8

After controlling for multiple other factors, women who were exposed to higher MF levels had 2.72 times the risk of miscarriage (hazard ratio = 2.72, 95% CI: 1.42–5.19) than those with lower MF exposure. The increased risk of miscarriage associated with high MF was consistently observed regardless of the sources of high MF. The association was much stronger if MF was measured on a typical day of participants’ pregnancies.

The paper notes that the study included 1054 pregnant women.  The study focussed on the highest levels of magnetic field exposure.  The paper claims that the study corrected for maternal age, race, education, smoking during pregnancy, prior miscarriage, maternal income, marital status, maternal nausea/vomiting, alcohol use, caffeine intake, maternal fever, vaginal bleeding, urinary tract infection, carrying loads > 10 pounds, exposure to solvents or degreasers, vitamin intake, and Jacuzzi/hot tub/steam room/sauna use during pregnancy.  They consider magnetic fields from all emitting sources, thus not specifically from WiFi and mobile phone use, such as the Mirror incorrectly claims.
Also from the paper:

Although we did not have information on the exact sources from which MF was generated, based on participants’ diary, we were able to examine whether MF exposure was from any of the following location categories: at home, at home in bed, at work, in transit, or from other sources. The association was observed consistently, regardless of the location.

This study thus did observe a correlation.  However, remember that correlation does not imply causation.  Critically, the paper does no attempt to suggest any physical mechanism that may cause the observed correlation.  Therefore, causation is not established.
I lack the medical domain expertise to otherwise judge the merits of the paper, but Scientific Reports is a reputable journal published by the Nature group, so there should be some peer review that filters out the junk (and the paper does not appear to be junk).  Note that Scientific Reports should not be confused with the actual journal Nature, which is much more prestiguous and harder to get into.  Finally, I will quote an insightful comment by MB made on the actual article:

The effect of the frequency of the magnetic field was not analyzed (which would be important to look for possible biomedical mechanism) and the frequency range of the device is not stated in the manuscript. Looking up the measurement device one finds a measurement frequency range of 40-1000Hz. Therefore only claims for this frequency range can be made. It is also surprising that the values reported are so small (range of a few hundred nano Tesla) - where even the solar radiation during strong magnetic storm are up to 500nT and also power lines, vakuum cleaner, hair dryer, etc typically produce way larger magnetic field.
  The authors do not even discuss this discrepancy in expected values and reported values.

Indeed, the range of 40–1000Hz has nothing to do with wifi or cellphones, so this does raise the question what exactly the authors are talking about.

P.S. Kudos to The Mirror for providing enough information to find the original article.

