I don’t know of a direct function to measure distance from a country, but I did need to do something very similar. This is how I did it:
1) I found a map file that gave the lat/lon of the county of interest. You can find help for Canada here:
2) I interpolated the segments that that no segment was too far apart from each other (“too far apart” is driven by your accuracy requirements). More points = more accurate at short distances
3) I calculated the distance from my input point to all these points using the distance function. The shortest value is your answer.
A more elegant solution may be to compare your input point against all the line segments rather than just the points defining your country outline.
