Starting with a question "What is it that the companies look for when they decide to sponsor an event?" I am quite sure the answers would be "Age of attendees, number of people attending (so they can figure out cost of reach (sponsorship amount / number of attendees), type of the event, general profession of attendees etc.).
Using that information you can build individual landing pages that speak to that particular type of the company.

For example, if you are trying to sell to a law firm, landing page that shows demographics from NYC LegalTech will go a long way.

Option number two (this worked for us, so I am not sure how it would translate) is finding a list of attendees from the particular conference and then creating demand by sending "These people are looking for solutions like yours" emails to decision makers at the companies you are targeting.

Hope this helps a bit. If we view this from a bigger picture perspective, you need to do what advertising industry has been doing for a while, and that is, you need to break down each event into key metrics and demographics and then use those to sell to the prospective sponsors.

We experimented a lot with the timing of tech and Entrepreneurship related events and early September would consistently bring us the highest quality of attendees.

Investors and senior partners generally do not like to travel during summer months and spend that time with their kids instead so they start traveling (enthusiastically) again in September once the kids are back in school.

Same goes for students, you will attract dramatically more students when the school is in session than during summer or winter breaks.

Source: I organized few conferences in the Atlantic region.