That's what picking a decent map projection is all about. I don't know your lat/long range but you can query projections relevant to a lat/long bounding box at the EPSG Geodetic Parameter Dataset. This should give some codes to test out.
EDIT: Thanks for posting your coordinates. When you just calculate a cartesian distance between these points in a Plate Carree or something similar projection, you get something like 90km which is obviously the wrong result from a wrong method.
Others have explained the 'math route' using a spherical calculation, so I took the 'tool route' and retrieved the ETRS89 projection from the EPSG database based on your coordinates, measuring in this coordinate system I get about 63km, which is the considerable difference we're seeing.