(Firstly, I am male!) My answer to the OP would be:... just time. And communication. Lots of it. In a way, some insecurity at the start may be a good thing, because it means you are aware that a relationship may end, rather than being in denial. As the saying goes, "always begin with the end in mind". Seeing through the anxiety may be what is needed, especially if the male partner has the patience to see it through. Being wary of partners who promise too much too soon.
The young lady who is now my DW did not feel secure at all when we first got together, three and a half years ago, she saw no future for us. At the time, she had almost no self esteem: she was recently out of her first relationship with someone who had no sense of responsibility, her own parents divorced, there were a lot of family issues. (We have no children.) When we met, her refrain was "you will be sick of me in six weeks", and whenever she got upset about anything, she would then say "you don't like me any more, do you?" It was very obvious she had "issues", but I decided to persevere with her.
At the start, before we lived together, I promised her nothing, but came to see her regularly, we went out together a lot. Eventually I relocated to move in with her. Although she would get upset from time to time, and her old fears of "being abandoned" would raise their head, I would remind her that it wasn't my spur of the moment decision to move in with her; I planned it very carefully, sold my old flat, moved my business, I would not make such a decision in haste, because I think she is worth it. On one occasion I complimented another woman on her outfit: she got very upset indeed and refused to speak all evening. Overnight she wrote me a long and apologetic note explaining exactly how she felt, how her former partner would totally ignore her to chat to women online, and her instincts got the better of her. (Some might think doing it in writing was a bit peculiar, but when she's upset she won't speak at all, and I think she found it easier that way. She said she could not promise never to be upset again, she could only try not to.) Upsets also happened once or twice when we hardly saw each other for a few days because of work.
All that was more than two years ago; we already have our first wedding anniversary behind us. We see the "jealousy and fear of abandonment" as something we have to live with, although it very rarely shows its head now. I get a bit nervous if I am working a lot and we don't see each other as much, and once I was in another town for several days at a time. We were both rather worried about how this would go, tensions were high beforehand, but afterwards all seemed fine. Sometimes I worry that resentment might be stored up to be spilled later, but I always communicate regularly with DW, ask her how she is feeling, we do many things together.