I'm indebted to Margaret Sykes of About Com for this excellent analysis.

Speaking of Beckwith and his essay "The Myth of Back Alley Abortions" Sykes says:
 

 

But wait a minute!  The whole point of this Beckwith essay is that illegal abortion was safe, mostly performed by physicians and hardly riskier than today.  But, you see, this puts "pro-lifers" in a serious bind. If abortion was very, very safe, then there were many, many abortions. And if abortion was rare, then it was very, very dangerous.  It cannot be true that illegal abortion was both safe and rare.  Here is the equation:
  

As you can easily see, because ND is a known constant, when NA is small, MR must become correspondingly big, and conversely when MR is small, NA must be big.  Both cannot be small.
 
Example: It's 1960.  ND = *250.  Let's make MR 50 times larger than today (a woman was 50 times more likely to die than now).  Since MR now is 0.3/100,000, that would be 15/100,000.  Then, solving for NA:

[* That's Beckwith's number - E]

                or  NA = (250)(100,000)/15 = 1,666,666 abortions 

1.67 million abortions per year in 1960?  If not, then abortion must have been even more dangerous.

But this guessing isn't necessary, because we actually know the mortality rate from abortion in the 1950s and 60s: it was about 20 to 25 deaths per 100,000 procedures from both legal and illegal abortion. ("Pro-lifers" are absolutely correct in saying that illegal abortion was not much more risky than legal abortion in those years; the greater risk from an illegal procedure was offset by the fact that women having legal procedures were sicker than women having illegal ones.  I will cite the references for this at the end.)  So, solving for NA is easy:
 
NA = (250)(100,000)/25 = 1,000,000
 
[editorial note: we can also deduce from this that the actual risk was about  75 times todays risk - E]    

And that's how we know that there were about a million abortions a year in the two decades before legalization.   Since we also know the number of legal abortions, less than 10,000 a year, we know the number of illegal abortions by simple subtraction.
 
Quoting Beckwith:

"Fourth, it is misleading to say that pre-Roe illegal abortions were performed by 'back-alley butchers' with rusty coat hangers. While president of Planned Parenthood, Dr. Mary Calderone pointed out in a 1960 American Journal of Health article that Dr. Kinsey showed in 1958 that 84% to 87% of all illegal abortions were performed by licensed physicians in good standing. Dr. Calderone herself concluded that '90% of all illegal abortions are presently done by physicians.'"

 That's right.  And that's how we have a good estimate of the risk of illegal abortion, and how we know that there were about one million abortions a year.  Interestingly enough, while "pro-lifers" like to cite Mary Calderone, they never mention that she also estimated one million abortions a year in the same article.

Example of dishonesty: writing that without admitting that Mary Calderone also estimated 1,000,000 illegal abortions per year in the very same article. (It's dishonest to present Calderone as an authority on illegal abortion when you don't also present other half of her claim.)

 Planned Parenthood held its conference on abortion in 1955. At that time the laws were so repressive that the conference was held in semi-secret and was not publicized.  This was not an unnecessary precaution. Medical and public-health professionals met at the conference which moved PP in a new direction under its courageous medical director, Dr. Mary Calderone.  The organization promised to keep the event quiet and told participants that they would be quoted only with their permission and could have their "participation deleted" from the published proceedings.  As Leslie Reagan points out in _When Abortion was a Crime,_ being associated with abortion in any way was dangerous.

In spite of this, the conference participants accomplished a great deal.  One of the accomplishments was the statistical committee which came up with the estimates of the number of criminal abortions.  It is this figure which is quoted in the NEJM article and in many others at the time and later.  But, as the JAMA article shows, this was not the only statistical estimate.  Besides the sources quoted in JAMA, there was also Christopher Tietze's estimate that "prior to the adoption of more moderate abortion laws in 1967, there were 1 million abortions annually nationwide, of which 8000 were legal, resulting in an abortion rate of 5 per 1000 people and an abortion ratio of 30 per 100 live births." This citation of Tietze comes from the Council on Scientific Affairs of the American Medical Association in their article "Induced termination of pregnancy before and after Roe v Wade," published in JAMA December 9, 1992.

You will find the "200,000 to 1,000,000" figure from the PP conference in many medical articles, but Tietze's 1 million per year is now considered most accurate.  (Tietze C.  "Abortion on request: its consequences for population trends and public health," Sem Psychiatry 1970;2:375-381.)
 
Now, here is the story on the decline in abortion-related mortality and how legalizing abortion saved women's lives.
 
This article is must-reading for anyone interested in the topic of illegal abortion:
 
"Legalized abortion: Effect on national trends of maternal and abortion-related mortality (1940 through 1976)."  Cates W Jr, Rochat RW, Grimes DA, Tyler CW Jr

 The authors found that pregnancy and childbirth-related deaths declined from 1940 to 1976 at an average annual rate of 13% per year before 1956 and 5% per year after that.  However, the abortion mortality ratio went through three phases: a steady decline from 1940 to 1950 at an average annual rate of 18%, reflecting the use of antibiotics and other advances in medical care; then a leveling off between 1951 and 1965 at an average annual decrease of only 1.8%; and then a suddenly improving decrease of 11% a year between 1966 and 1970 followed
by a decrease of **25% a year between 1970 and 1976.

      Year  Births  Birthrate

      1973  3,136,965  14.9
      1974  3,159,958  14.9
      1975  3,144,198  14.8
      1976  3,167,788  14.8
      1977  3,326,632  15.4
      1978  3,333,279  15.3
      1979  3,494,398  15.9
      1980  3,612,258  15.9