Today was my oath ceremony and I will be traveling to Canada (birth country) by car in a couple of days from now. Would I be able to cross the border into Canada from the U.S. with just my Canadian Passport and my Certificate of Citizenship? Same goes for the other way around. Thanks in advance.
- Entering Canada on your Canadian passport. No problems here. Canada recognizes dual citizenship, you didn't lose your citizenship. (I am a Canadian-Hungarian dual citizen, I am familiar with these things.)
- Entering the USA with your certificate. This is where the fun starts. Leave plenty of time for this. The law says you must use your USA passport to enter into the USA if you are a US citizen but all penalties for breaking it were removed decades ago. And, no country can deny entry to their citizens, that's the very definition of citizenship. So, you will show up at the border, explain the situation, provide the Canadian passport as an identification document, the USA citizenship certificiation as proof you are a USA citizen. They will verify the latter somehow and let you in. Depending on their mood you might get a stern talk as well. Oh well. Get a passport next time, right now there's just not enough time it seems (it takes 8 business days for an expedited passport to go through right now). Of course, if you are travelling for a Life-or-Death Emergency then you can get a passport almost immediately. Once you got your passport, make sure to put the certificate away well, it's a very important, very hard to replace document. A bank safe or your bug out folder of documents (if you have one prepared) is the right place for it.
If this is via air, say nothing to the airline. Your Canadian passport is enough to enter the USA (Canadians don't need an ESTA as you very likely know) and that's it. Hold palaver only with the CBP.
Exception Canada: Dual Canada/US citizens may enter with a US Passport, but you may have to bring your Canadian Passport with you (see first link).
Your US Certificate of Citizenship will serve as proof of your US Citizenship on reentry to the US, but should be considered a valuable document that should be stored safely if/when later needed.
Consider applying for a US Passport Card for future use, avoiding a possible loss or damage of the Certificate, which may be difficult to replace if lost or otherwise unreadable.