The containers.Map object is a Matlab object like any other.  Under the hood these are implemented as a Matlab structures with some additional access controls and function mappings.  
You can force Matlab to show you the raw structure using the struct command.  This throws a warning, as it is usually not recommended.  However, the structure view of the class shows the complete contents, and is accurately reflected in a whos call.
Some example code is below: 
%Initialize map and add some content
res_Map = containers.Map;
for ix = 1:1000
    res_Map(sprintf('%05d',ix)) = ix;
end
%Look at the memory used by the map
disp('Raw who:  always 112 Bytes for Map')
whos('res_Map')
%Force the map into a structure, and look at the contained memory
mapContents = struct(res_Map);
disp('Look at the size of the map contents, reflect true size')
whos('res_Map','mapContents')
%Add additional contents and check again.
for ix = 1001:2000
    res_Map(sprintf('%05d',ix)) = ix;
end
mapContents = struct(res_Map);
disp('Look at the size of the map contents, reflect true size')
whos('res_Map','mapContents')
The result of the above script (after removing the warning messages) is shown below:
Raw who:  always 112 Bytes for Map
Name            Size            Bytes  Class             Attributes
res_Map      1000x1               112  containers.Map
Look at the size of the map contents, reflect true size
Name                Size             Bytes  Class             Attributes
mapContents         1x1             243621  struct
res_Map          1000x1                112  containers.Map
Look at the size of the map contents, reflect true size
Name                Size             Bytes  Class             Attributes    
mapContents         1x1             485621  struct
res_Map          2000x1                112  containers.Map