My assumption is based on the dynamic of Southern slave society and culture, where white female miscegenation was a grievous social outrage, though the ultimate victim was usually the male involved in the "violation", but the regular abuse of slaves by white males was usually, at worst, an open secret. Nazi and German men's abuse of minorities, enemy or occupied peoples seems ubiquitous and not often remarked upon - logistical and bureaucratic instruments like the Ausländerkinder-Pflegestätten were established just to deal with the consequences (you may not want to look those up if don't want to be upset).
How often did German women who violated the anti-miscegenation laws "make the news"?
This is a real interesting but also very broad topic. There are several different situations to be taken into account.
First there are marriages between gentiles and jews that had been wed until 15. September 1935. In the so called 'Mischehen' ('mixed marriages') the jewish partner was - compared to other 'Volljuden' ('full/complete jews') - in a privileged situation insofar as they were exempt from deportation until very much the end of the 3rd Reich, also from wearing the Yellow Badge and, depending on the Gau ('province'), the couples had better food supply. That was decreed in December 1938. Before that they were treated as bad as 'Volljuden', but before that there were also no deportations on racial grounds, no Yellow Badges and no food rationings. Well, exept from 9. November 1938 on, that is.
Those marriages were divided into 'privileged' and 'non-privileged' marriages.
'Privileged' were those, where the wive was jewish or existing children were raised as christians. Since your status as a 'Jew' didn't depend so much on your religious beliefs but on the beliefs of your ancestors that might have been more often than you might think. The 'privilege' of those couples was that they could stay in their houses/appartments and that the 'jewish' partner could transfer their properties to the gentile partner, so that those wouldn't be seized during any anti-jewish actions.
'Non-privileged' were those, were the husband was jewish and there were no children existed or existing children were raised as jews or where the gentile partner had converted to judaism. Those had to move into 'Judenhäuser' ('jew houses'), some kind of ghettos, and their accounts would be blocked.
So in a sense you could say, that gentile german women were more punished than men (but also, that jewish *men* were more punished than jewish women). Then there's also the fact, that far more gentile women had married jews than men had (afaik the quote was about 3:1), and that they also had converted more often to judaism.
http://www.dasjuedischehamburg.de/inhalt/mischehen-%C2%BBmischlinge%C2%AB
But always the 'race' is by far more important than the sex of a person (see also Goldhagen, Daniel Hitler's Willing Executioners or Kogon, Eugen Der SS Staat on this), and since men were deemed to be the 'active' part in sexuality it's usually men who were punished more harshly, just as the Nazis persecuted male homosexuals but not female ones.
All this, of course, didn't safe involved women from spite and hatred of their neighbors etc.
But I digress.
Since new weddings between 'jews' and gentiles were illegal from 15. September 1935 on any relationship between them, even a kiss, even if they were engaged, was deemed to be 'Rassenschande' ('race disgrace') that was punishable only for men. But again the penalty for jews was by far more serious than for gentiles. While gentiles would usually be sentenced to up to 5 years in prison jews would get up to 15 years penitantiary (which would very often be a death sentence since GeStaPo would put them into concentration camps, that weren't necessarily extermination camps but very lethal for jews anyway) or a death sentence right away (against actual law). The involved women were persecuted on grounds of perjury if they made any attempt do defend the jew, usually for about 2 years penitatiary.
http://www.bpb.de/izpb/137221/verfolgung?p=4
https://www.ns-archiv.de/system/justiz/katzenberger.php
If they were german. If they were foreigners - especially slavics - or jews the women would be taken into 'Schutzhaft' ('preventive arrest') that would very often also mean death in a concentration camp. And again, there was no lack of people who would treat the german women with spite and hatred in any way.
I guess you have seen those pictures with people wearing placards around their necks with slogans on them (often it was 'Ich bin im Ort das größte Schwein, ich lasse mich mit Juden ein' ('I'm the worst pig in town, I intermingle with jews') for the women and 'Ich nehm als Judenjunge immer nur deutsche Mädchen mit auf's Zimmer' ('I take as a jewish boy always only german girls with into my room') for the men. That was thought to be funny, especially since it rhymed). Those were often posted in local newspapers, sometimes there were also just small adds, telling the name of a gentile woman who had been committing 'Rassenschande' with a jew (or foreigner) whose name would also be told. I don't know how often this exactly happend, I'm not even sure, if this has been researched in detail, but it happend often.
Then there was the case of the foreign laborers of whom there were a lot in Nazi Germany during the war. Since the men were often in the war and the women not it's no surprise that women ended up far more often in relationships with those than men, especially if they had a farm and were thus or any other way in a close employment relationship with them, so they were more often persecuted for 'Rassenschande' with them than men. (But there was of course a difference if the men were e.g. polish or dutch)
For the men in the war, and here it really gets sexist, the whole thing was different. Many germans in the occupied territories had mistresses or frequented prostitutes (there are estimates of about 1 - 2 million children from german soldiers with women in those territories), what wasn't seen as a problem by the superors, but lead to acts of aggression against those women once the germans had to retreat from those regions.
https://zeithistorische-forschungen.de/2-2004/id=4594
https://web.archive.org/web/20091130210828/http://www.tagesschau.de:80/ausland/meldung235098.html
According to Welzer, Harald Täter. Wie aus ganz normalen Menschen Massenmörder werden (*Perpetrators. How normal humans become mass murderers') it was even quite common for the SS men to use jewish women for sex and letting them believe that this would save them somehow and shoot them afterwards anyway.
So let's end this post with a very disturbing quote from said book (my translation):
'As I opened the door to the room, I saw an SS man lying there, having a young pretty girl with him. Since this SS man couldn't tell me, where [Hauptsturmführer] Finger was, I went into a second room. In this room, again, I found a girl with an SS man. Since I here also couldn't find my information I went into a third room. In this third room on the bed lay an SS man without uniform but with his trousers on. Besides him [...] sat again a young, very pretty girl, and I saw, how she caressed his chin. I also heard the girl say: 'Yes, Franz, you won't shoot me!' That girl was still very young and she spoke german without any accent. [...] I asked the SS man, if this girl, of whom I thought, she was a jew, [,,.] in actuality would be shot. The SS man told me, that all the jews would be shot, without any exception. I asked further, what would happen to the girl I had seen in this room. The SS man said something to the effect, that this was bitter. Sometimes they would have the opportunity to hand those girls to a different death squad, but most of the time there was no time for this and they had to do it themselves.'
PS: Most my sources are in german, sorry, but I guess considering the topic this might be inevitable