We recommend looking at your results at least a few weeks after the post goes live to get a more accurate indication of volumes.
The success of your collaboration is tricky to define as your goals will be different for each collaboration you send. (eg was your goal to increase brand awareness, generate a good backlink, gain new instagram followers, generate engaging content or increase sales of a particular product for example)
Some methods of measuring your results:
Ask the blogger to provide you with stats on the number of post views.
Social Media posts:
Once links have been added (by yourself or the influencer) to your Report page, stats will be viewable there (help article) without needing to contact the influencer including volume of likes and comments.
You could contact the influencer for additional info about the total reach per Instagram or Twitter post.
Keep an eye on an increase of followers and engagement on your own channels.
Check your site traffic to observe the traffic from the influencer’s post. This may appear as coming direct from their blog, or just a direct search of your URL or brand name.
Check your sales stats for a peak around the time of the post