Implementing a child theme without loosing settings

I have tried couple of times to create a child-theme to my WP-installations. I always confront the same problems:

I create a basic child-theme by making a child-folder and creat a style.css-file where I import the maintheme’s style.css.
After this I take the child-theme to use. What happens is this:

All the widgets are erased
With some themes also the page settings are erased.
Theme options are erased (for example custom-logo etc)

Seems to me that when the child theme is taken is use then at least I need to take the main menu in use again and to set the mainpage, or is there any way to keep these settings so that they are not erased? How about those widgets and theme options and so on? Is there a way to keep everything as they were after activating the child-theme?