We de­scribe both an­a­lyt­i­cal­ly and nu­mer­i­cal­ly beams ra­di­a­tion in pres­ence of media which can be re­al­ized as mod­ern meta­ma­te­ri­als. In par­tic­u­lar, ef­fects of re­versed Cherenkov ra­di­a­tion (RCR)* and re­versed Cherenkov-tran­si­tion ra­di­a­tion (RCTR)** are con­sid­ered. These phe­nom­e­na can be used for de­tec­tion of charged par­ti­cles and di­ag­nos­tics of beams. Ear­li­er we noted some use­ful prop­er­ties of ra­di­a­tion in the case of the bound­ary be­tween an or­di­nary medi­um and an isotrop­ic left-hand­ed meta­ma­te­ri­al (LHM)*. Now we con­tin­ue to an­a­lyze prospects of use of LHM for beam di­ag­nos­tics. More­over, we in­ves­ti­gate RCR and RCTR in the case of cer­tain anisotrop­ic ma­te­ri­als with prop­er­ties being sim­i­lar to prop­er­ties of LHM. The use­ful fea­tures are re­versed char­ac­ter of ra­di­a­tion and, par­tic­u­lar­ly, ex­is­tence of two thresh­olds for RCTR (lower thresh­old and upper one). This fact al­lows se­lec­tion of par­ti­cles (or beams) with en­er­gy in some pre­de­ter­mined range. The spe­cif­ic ra­di­a­tion pat­terns (hav­ing two or three lobes in anisotrop­ic meta­ma­te­ri­al) can be use­ful for par­ti­cle en­er­gy mea­sure­ment as well.