Did the United States (particularly in the 20th century) ever impose any trade embargoes on the basis of health related concerns? Are there instances where the U.S. said that if Country X doesn't meet particular health standards, it will limit trade with said country?
Yes, there is at least one example below.
As of June 21, 2011, the US had partial trade embargoes, issued by the CDC, on the import of birds from the following countries due to the H5N1 virus (bird flu):
East Asia and the Pacific:
- Hong Kong
- South Korea
Europe & Eurasia:
- Burkina Faso
- Ivory Coast (Cote d’Ivoire)
- South Africa
- Palestinian Autonomous Territories
- Saudi Arabia
These have since been rescinded.
According to Princeton WordNet, a trade embargo is a government order restricting international trade. Wikipedia says that such embargoes can be partial embargoes, such as Princeton WordNet's import barrier. A country may choose what and how many items are excluded in a partial trade embargo. In the above case, the partial trade embargo restricts just the import of birds into the US.
No, there are no instances of "Country X does not meet health standards" leading the United States to stop trade with that country.
There are however plenty of cases when the United States (and also other countries) have stopped imports of particular products from particular because of health concerns. Countries where there are outbreak of "mad cow disease" will typically see other countries shutting down import of beef, as an example.