Biggest piece of advice I can give is
DON'T BE AFRAID TO ASK. The worst a they can do is say "no."
A good place to start looking when it comes to sponsorship is team parents. A lot of companies have money set aside for organizations their employees volunteer with. Having a team members' parent employed at a potential sponsor's company (especially if they are willing to mentor) is a good way to get your foot in the door. Similarly if any parents know someone who works for an engineering company that would be willing to mentor, that is another great way to get sponsors on board. After that I would recommend looking at any companies that are located locally - not just the Lockheeds and Microns though, small ones too.
As far as getting the "yes," it might be helpful to work up some kind of informational handout for your sponsors that tell them what you are all about and how they can benefit from a relationship with your team. Offer to put their logo on your robot, offer to come demo your robot at their office, or host some kind of sponsor dinner - get creative with it. If they offer a lot maybe you could even figure out a way to incorporate their name into yours ("Baxter Bomb Squad"). Panthrobotics has a nice sponsor information packet
here that could be a good place to start. Feel free to PM me if you need any help
.