If you don't have the EIN or SSN of the person/entity you are issuing the 1099-MISC to, you will be fined by the IRS. Use the form W-9 to get what you need.
https://www.irs.gov/pub/irs-pdf/fw9.pdfFill out what you can and send it certified mail, return receipt *required* (not requested)
If the requested information isn't provided in 10 days, you can issue the 1099-MISC without it, but you will not be able to e-file it (unless you want to pay a penalty). You'll have to print and mail it in to the IRS along with your proof of attempt to obtain the EIN/SSN. Include a copy of the W-9 along with copies of the signed receipt confirming the recipient received your W-9 request.