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I had this issue, and fixed it by setting the GDAL_DATA variable correctly, so that fiona can map the projection strings correctly. For reference, I'm using Anaconda, the Spyder IDE, Fiona 1.8.4, and Python 3.6.8, and GDAL 2.3.3.

While Anaconda usually sets the GDAL_DATA variable upon entering the virtual environment, using another IDE like Spyder will not preserve it, and thus causes issues where fiona can't export the CRS correctly.

You can test this fix by trying to printing out a EPSG to WKT transformation before & after setting the GDAL_DATA variable explictly.

Without setting GDAL_DATA:

import os
print('GDAL_DATA' in os.environ)
from osgeo import osr
srs = osr.SpatialReference() # Declare a new SpatialReference 
srs.ImportFromEPSG(3413) # Import the EPSG code into the new object srs
print(srs.ExportToWkt()) # Print the result before transformation to ESRI WKT (prints nothing)

Results in:

False

With setting GDAL_DATA:

import os
os.environ['GDAL_DATA'] = 'D:\\ProgramData\\Anaconda3\\envs\\cfm\\Library\\share\\gdal'
print('GDAL_DATA' in os.environ)
from osgeo import , osr
srs = osr.SpatialReference() # Declare a new SpatialReference 
srs.ImportFromEPSG(3413) # Import the EPSG code into the new object srs
print(srs.ExportToWkt()) # Print the result before transformation to ESRI WKT (prints nothing)

Results in:

True
PROJCS["WGS 84 / NSIDC Sea Ice Polar Stereographic North",GEOGCS["WGS 84",DATUM["WGS_1984",SPHEROID["WGS 84",6378137,298.257223563,AUTHORITY["EPSG","7030"]],AUTHORITY["EPSG","6326"]],PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],UNIT["degree",0.0174532925199433,AUTHORITY["EPSG","9122"]],AUTHORITY["EPSG","4326"]],PROJECTION["Polar_Stereographic"],PARAMETER["latitude_of_origin",70],PARAMETER["central_meridian",-45],PARAMETER["scale_factor",1],PARAMETER["false_easting",0],PARAMETER["false_northing",0],UNIT["metre",1,AUTHORITY["EPSG","9001"]],AXIS["X",EAST],AXIS["Y",NORTH],AUTHORITY["EPSG","3413"]]