I would not recommend to call them. First it is very intrusive, second if i had a call from every product's company I had a trial for (consider me now as a SMB guy that tried a lot of tools), I would stop the call very soon because I'm yet on the phone all day..
Here are a few ways to increase your conversion rate:
1) Marketing Intelligence (=automated interactions)
Do you precisely track what your trial users do with your product? Today tools exist to do so (Totango, Apptegic, you could even do it manually with some GA stats or an in-house tool but it would be more work...). Track what they do, then extract lists of users and send them some very targeted emails.
An example: let's say you have functionalities A and B in your product.
Get lists of users who did A but not B and send them an email saying: "You did A with our product, why not trying to do B now?" with a direct link to the B functionality. And the same for those who did B but not A, with a dedicated email.
After that, when users did not use the product since a long time, why not send them a reminder: "Hey, we didn't see you for a long time, why not come back?"
And so on.. you have to define what is the ideal way to go from free to premium in your product (that's called a funnel), and then speak to users that are not going through the defined way.
One thing very important about all these mails is to let users unsubscribe from these reminders (for legal reasons first, and because some people may be very annoyed by your emails).
Do you have welcome cycle, tutorials, video explainers, extended help page to help your users get your product working? If not, it's another part of the marketing intelligence. You can even send them an email: "you didn't go through our tutorial/welcome cycle, why not doing it now?"
It's all about taking your users by the hand.
2) Surveys/feedback (= marketing intelligence too, but for product improvement)
Maybe your users had problems using your product but did not have time/way to tell you. Do you have visible feedback buttons/forms in your product for them?
Do you have a survey (not a big one) to let users share their point of view? If not, create one now, you'll have more precious feedbacks. And you can still mail them to ask them to fill the survey (ONLY if they didn't yet, that's why tracking is very important: if they yet filled the survey they would not understand why they get this message).
Before adding more and more functionalities, the existing ones must be perfect, and your users must have a way in the product to express their thoughts very easily about their problems/ideas. Surveys and feedback forms are the good way for that.
3) Forget them? (= acquisition/concentrate on getting more targeted users)
Ok, this one is not intended to increase conversions.
If you consider your conversion rate is low, maybe it's because your users are not the ones really willing to use your product. In my case, I subscribed to a lot of trial periods on a lot of products just to test them, get new ideas, check competitors, or just to have fun trying a new thing. But for most of them, I knew since the very beginning I will never actually buy them.
So, maybe you should try to get more targeted users. Try to reach the people that would really consider buying your product, and forget the others. The ways to do so is public relations, ads, presence at meetups specialized in your market, and more. But all of these have to be well done to not loose time and money:
- for PRs, only target the journalists/bloggers specialized in your domain, not the others
- for ads, only use very targeted keywords, on very targeted websites
- for meetups/conferences, don't loose time in those that you think you have only a few chances to reach new users
And there is an hundred more ways to get targeted users, I can't list all of them here, it would be too long.
All of those ways I spoke about are cumulative, you should start all these actions at the same time, each of them will slightly increase your conversion rate.
At last, remember that conversion rates are never very high, you'll have to gain your premium users one by one.