I changed the hosting of my B2Evo blog to SSL. The only necessary configuration change was the $baseurl in conf/_basic_config.php. But there remained an issue with mixed content. Images of posts were still rendered by http, because the image links are hard-coded in the database. The following query helped:
UPDATE evo_items__item
set post_content = REPLACE(post_content, 'http://www.fabianfier.de',
'https://www.fabianfier.de')
where post_content LIKE '%http://www.fabianfier.de%';