In the field of energy harvesting, recycling the energy of mechanical vibrations from the environment becomes an attractive option to use in low power applications. With this goal, mechanisms of transduction have been developed with electrostatic, piezoelectric and electromagnetic principles of operation. In this work we present the analysis for an electromagnetic micro-generator using the linear generator approach combined with the dependence of the electromotive induced force (EMF) with geometrical parameters such as the radii of the coil and the magnet, the distance between them, and the "slope" of the coil, a parameter representing the reduction of radii as a function of each turn of the helicoidal winding. The latter feature introduces the possibility of pyramidal coils instead of solenoidal coils. We show that when the distance between the coil and the magnet is of the order of the radius of the magnet, the pyramidal geometry presents a higher induced electromotive force than a solenoidal coil of comparable dimensions. We also illustrate a method for the construction of a micro-electromagnetic generator which contemplates the fabrication of pyramidal coils with tridimensional electron beam lithography. Results for resonant structures and microcoils are discussed. The estimated induced EMF and power were calculated for a pyramidal high density coil generator, showing a better performance for the pyramidal when compared with the solenoidal geometry.