There is a delicate line between pitching your expertise and offering your help. There are subtle behaviors in walking that line ~ without giving away too much information (or strategy or resolution) and engaging your prospect with full understanding of your value.
The approach must be: “I’m here to be of service…. to help/ to explore / to see if my expertise can be of any help to you /your dept / your team.”
You must not act like a vendor selling your wares or competing with “bids” on an open Request for Proposal.
You must not need anything (even if you are desperate for paying gigs).
Do not pitch. Again, do not pitch. Instead, offer something of value — a new direction in approaching the prospect’s problem (but not the solution itself), or a success story you once resolved for a similar problem.
The prospect interview (the first, perhaps also the 2nd or 3rd) should be a direct demonstration of your expertise, essentially, a small consulting meeting. The prospect cannot know the value of your services unless he/she experiences the effects of that value. You need to give some stuff away.
Here is that fine line you must learn to navigate. You do not offer the final resolution to the problem, or the strategy itself. But by the questions you ask, and the suggestions you make, and the brief success stories you share, you show your prospect how you think, how you approach the problem, what questions to ask to get to the next steps, and so on. Many of these suggestions may (should) need your further participation to be effective.
Essentially, you must “step back” (from pitching) so that your prospect has enough space to “lean forward” to ask for more from you — more thoughts, more expertise, more co-dependence, more work (under contract).
Successfully walking this line comes with experience. The first step is to realize that you must assume this position when speaking with potential clients, and be aware of this “positioning” at all times.