An elongate medical device having a body with proximal and distal end portions, comprising: a sensor disposed at said distal end portion, said sensor including (i) an electrically insulative, flexible substrate in a three-dimansional form and having a non-flat, curved surface; and (ii) an electrically-conductive trace disposed on said substrate and comprising start and end leads (54, 56) wherein said electrically-conductive trace disposed on said substrate includes said start and end leads, said substrate and trace being configured so as to form a plurality of turns between said start and end leads (54, 56), said sensor being configured to detect a characteristic of an electromagnetic field and produce a signal indicative of said characteristic, wherein said start lead is at a proximal end of said sensor, said end lead returning from a distal end of said sensor to said proximal end of said sensor and being electrically insulated with respect to the trace such that both of said leads appearing at said proximal end of said sensor, the plurality of turns defining a plurality of trace sections, each trace section defining an advancing section, a parallel returning section and an intervening section connecting the advancing section and the returning section, wherein a spacing between the trace sections is less than a width of one of said plurality of trace sections of said trace taken into longitudinal direction and constant across the trace; a cable comprising a pair of electrical conductors (701, 702), wherein each conductor is coupled to one of said start and end leads (54, 56), said cable extending through said device to said proximal end portion thereof, said cable being configured for electrical connection to a positioning system. a sensor disposed at said distal end portion, said sensor including (i) an electrically insulative, flexible substrate in a three-dimansional form and having a non-flat, curved surface; and (ii) an electrically-conductive trace disposed on said substrate and comprising start and end leads (54, 56) wherein said electrically-conductive trace disposed on said substrate includes said start and end leads, said substrate and trace being configured so as to form a plurality of turns between said start and end leads (54, 56), said sensor being configured to detect a characteristic of an electromagnetic field and produce a signal indicative of said characteristic, wherein said start lead is at a proximal end of said sensor, said end lead returning from a distal end of said sensor to said proximal end of said sensor and being electrically insulated with respect to the trace such that both of said leads appearing at said proximal end of said sensor, the plurality of turns defining a plurality of trace sections, each trace section defining an advancing section, a parallel returning section and an intervening section connecting the advancing section and the returning section, wherein a spacing between the trace sections is less than a width of one of said plurality of trace sections of said trace taken into longitudinal direction and constant across the trace; (i) an electrically insulative, flexible substrate in a three-dimansional form and having a non-flat, curved surface; and (ii) an electrically-conductive trace disposed on said substrate and comprising start and end leads (54, 56) wherein said electrically-conductive trace disposed on said substrate includes said start and end leads, said substrate and trace being configured so as to form a plurality of turns between said start and end leads (54, 56), said sensor being configured to detect a characteristic of an electromagnetic field and produce a signal indicative of said characteristic, wherein said start lead is at a proximal end of said sensor, said end lead returning from a distal end of said sensor to said proximal end of said sensor and being electrically insulated with respect to the trace such that both of said leads appearing at said proximal end of said sensor, the plurality of turns defining a plurality of trace sections, each trace section defining an advancing section, a parallel returning section and an intervening section connecting the advancing section and the returning section, wherein a spacing between the trace sections is less than a width of one of said plurality of trace sections of said trace taken into longitudinal direction and constant across the trace; a cable comprising a pair of electrical conductors (701, 702), wherein each conductor is coupled to one of said start and end leads (54, 56), said cable extending through said device to said proximal end portion thereof, said cable being configured for electrical connection to a positioning system.