Having guided several companies through the same exact problem, I'll say that there are practical ways to tackling this problem. In fact, the same solution applies to finding a non-technical cofounder, key employees or even adding people to the overall team.
The key lies in focus. You need to first figure out what expertise you possess. Then clearly identify what problem your startup is tackling. Then, you need to approach people who worked (or work) in top companies closer to your focus area and complement your expertise. Your startup must have a clear focus to succeed not only in attracting talent but in just about any stage of the venture. So focus is essential.
Once you're clear on what you know and what you want to do, it's not that hard to research companies that tackle similar problems. LinkedIn is an amazing place to start your research. You can easily connect with the people you found through common connections or the InMail functionality. Another great resource is data.com which used to be called JigSaw. If you know who you want to work with but don't know their email, try data.com. It's quite likely that you'll find their contact information. If you're working on something very technical, then research academic papers or patent filings. You should be doing this anyway. Keep track of other people who have worked on these. Contribute to working papers if you can. These places provide you with SOLID contacts within the domain of your problem but again, you must be clear about the problem.
Now these resources make information available and enable your first touch. But you have to be brief, honest, and humble in your inquiry. Ask for a brief call or a cup of coffee. If they accept, great, again, keep it nice and short and to the point. Engineers are pretty analytical and straightforward people. If they like you, they do, if not then not. Stay in touch and exchange ideas from time to time. Perhaps you can tackle a problem via email for a while. It's about building relationships from there. Study the art of building relationships and work on it every day.
Remember, everyone wants to connect and grow. And everyone can be a bit anxious and scared as we all are from time to time. So approach technical people with respect and at the least, you'll make a new friend.