I looked for a couple websites that would give out ZIP codes by county. The first two I found were GetZIPS.com and MelissaData.com.
I tend to trust Melissa more.
Looking for ZIP Code 12309, primarily a ZIP Code in Schenectady, I wanted to see if the small portion in Albany County in that ZIP would show up. Yes in Melissa;, no in GetZIPS.
Remember that ZIP Codes are no respecter of county boundaries.