How charities can effectively engage brands?
I have recently created a project which helps a lot of women who have experienced domestic violence. 
Women work in various spheres of life and I understood that an important part of our work was to find and offer cooperation to brands. 
Why did I think this was important?
All big brands invest in people with the help of advertising. They had already cooperated before. Brands have become media channels for people. Sometimes people trust brands more than simple media channels, because brand marketing adapts to people's opinion and tries to win their wallets.
I understood we could find people there, because in addition to help it was important to tell all people about this huge problem.
We also decided to create a media platform. My strategy was to organise special projects with brands, which included elements of performance such as exhibitions, photoshoots, online lectures, flash-mobs, etc. with brands and invited their target audience.
We have built an ecosystem where women, who suffered from domestic violence, could get help from psychologists and employers, but besides they were involved in the agenda and help each other themselves.
We were finding brands’ customers who would appeal to our topic. We organised some interactive activities which could bring up this problem for discussion.
What do brands get from cooperation? Below I demonstrate some important things that you can use in communication with marketing departments.

Difficulties arise when you think that brands owe you something. This is not a very good idea. Try to find areas of common interest where you can be in «win-win» position.
What can I recommend?
Demonstrate the statistics of your project and its influence on the target audience. If you have social media you can use its statistics in your presentations. You have to think as a marketing manager. For example, we offer brands to launch a project where we can help with psychological consultations to brands’ customers.
For all our special projects we created a landing page where we can put brands’ logos. We openly demonstrate cooperation with brands and speak about it with our audience. After some time they started to trust us. It took some time.
Use your platform with useful for target audience in every project. We also use warming up our audience like many inline projects, but we differ in that we do not ask for money for the benefit.
Before offering something for brands you can do some work, for instance, you could found influents people with big audience in social media who could be interesting for brands. It will give chance for negotiations.
If you want to check out the project you can open the website: