Hi Marta, I can relate—I have a graphic design background in print design as well, but these days I do more website design and project management.
The challenge is that many companies have grown from an entrepreneur start, and often the, "if it isn't broke, don't fix it attitude prevails, and when a designer is contacted for a project, cost concerns always trump the actual results.
Larger companies with communication departments or marketing departments tend to be better potential clients as they understand better the role of a graphic designer better.
Micro businesses are the most challenging as they are always cash strapped, and even though they know they need a professional's touch, they may not have the budget to do so.
Over the years I have had several graphic strategic partners and lead providers such as printing companies, public relations professionals and clients who knew me and my work and would send me great referrals. These type of relationships take a while to develop, but almost all the referrals turned out to be highly pre-qualified clients who respected what I did because the person making the referral had their respect.
Making contact with and developing strategic partnerships can take a while, but can mean getting in front of much better clients. If you take this approach, make sure you seek out people who understand what you do, but also that they understand they are not "selling you" as a salesperson, but are just recommending you as the right person for what the client needs.
Lastly, I developed a marketing questionnaire over the years that I ask prospective clients to complete during the discovery process. This can be a great tool to weed out prospects. After talking to a new prospect and getting an idea about their project or needs, I send over the questionnaire by email. Typically those who complete the questionnaire turn out to be better long-term clients. Those prospects who don't want to take the time to fill out the questionnaire usually aren't that serious about working with professionals.