<PAGE>
                                                                     EXHIBIT 4.2
 
                               WARRANT AGREEMENT


     This WARRANT AGREEMENT (the "Agreement") is entered into as of March 12,
1999 by and between Evercom, Inc., a Delaware corporation (the "Company") and
SHAREHOLDER~ (the "Holder").

     Contemporaneously with the execution of this Agreement, the Holder has
agreed to acquire SHARES~ shares of the Company's First Preferred Series A
Stock, $0.01 par value stock ("First Preferred Series A") and, in connection
therewith, the Company has agreed to issue and sell to the Holder a Warrant, as
hereinafter described (the "Warrant"), to purchase SHARES~ shares (the "Shares")
of the Company's Class A Common Stock, $0.01 par value ("Class A Common"). The
issuance of the Warrant by the Company shall occur concurrently with the
Holder's acquisition of the shares of First Preferred Series A Stock.

     In consideration of the foregoing and for other good and valuable
consideration, the receipt and sufficiency of which are hereby acknowledged, and
for the purpose of defining the terms and provisions of the Warrant and the
respective rights and obligations thereunder, the Company and the Holder hereby
agree as follows:

     1.   Transferability and Form of Warrant.
          ----------------------------------- 

     1.1. Registration.  The Warrant shall be numbered and shall be registered
          ------------                                                        
on the books of the Company when issued. This Agreement, the Warrant and any
Shares issued hereunder are subject to the rights and obligations of that
certain Shareholders Agreement (the "Shareholders Agreement") dated as of
December 27, 1996, between the Company, and the shareholders and warrantholders
of the Company.
 
     1.2. Non-Transferability.  The Warrant may be freely traded separate and
          -------------------                                                
apart from the shares of First Preferred Series A. However, neither the Warrant
nor the right, title or interest of the Holder in this Agreement may be
transferred or assigned unless such transfer or assignment is to an "accredited
investor," as defined in Rule 501 promulgated under the Securities Act of 1933,
as amended, compliance with said standard to be demonstrated by evidence
reasonably satisfactory to the Company; provided, however, in the event the
                                        --------  -------                  
Holder assigns or transfers its interest in this Agreement, the assignee or
transferee of said interest shall be subject to all Section 1.3 restrictions and
shall acquire only such partial exercise rights as remain pursuant thereto. This
Agreement and all rights and interests hereunder are assignable or transferable
by the Holder only in whole and not in part. Any Shares issued pursuant to a
Warrant issued hereunder shall be subject to the rights and obligations of that
certain Registration Rights Agreement dated as of December 27, 1996, between the
Company and its shareholders and warrantholders, and the Shareholders Agreement.
 
     1.3. Securities Law Restrictions on Transfer of the Warrant.  Neither this
          ------------------------------------------------------               
Agreement, the Warrant, any of the Shares, nor any interest herein or therein
may be sold, transferred, or 

                                      -1-
<PAGE>
 
otherwise disposed of in the absence of registration or qualification, as the
case may be, of the same under the Securities Act of 1933, as amended, and
applicable state securities laws, or an exemption therefrom. The Warrant may be
divided, upon request to the Company by the Holder, into a certificate or
certificates representing the right to purchase the same aggregate number of
Shares. Unless the context indicates otherwise, the term "Holder" shall include
any transferee or transferee of the Warrant and the term "Warrant" shall include
any and all warrants outstanding pursuant to this Agreement, including those
evidenced by a certificate or certificates issued upon division, exchange,
substitution or permitted transfer pursuant to this Agreement.
 
     1.4. Form of Warrant.  The text of the Warrant and the form of election to
          ---------------                                                      
purchase Shares shall be substantially as set forth in EXHIBIT 1.4A and EXHIBIT
                                                       ------------     -------
1.4B attached hereto and hereby made a part hereof. The Warrant shall be
----                                                                    
executed on behalf of the Company by its Chairman, President or any Vice
President.
 
     A Warrant bearing the signature of an individual who was at any time the
proper officer of the Company shall bind the Company, notwithstanding that such
individual shall have ceased to hold such office prior to the delivery of such
Warrant or did not hold such office on the date of this Agreement.
 
     The Warrant shall be dated as of the date of signature thereof by the
Company either upon initial issuance or upon division, exchange, substitution or
transfer.
 
     1.5. Legend on Warrant Shares.  The Warrant and each certificate for Shares
          ------------------------                                              
initially issued upon exercise of the Warrant, shall bear the following legend:
 
          "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT").
SUCH SECURITIES MAY NOT BE SOLD, ASSIGNED, TRANSFERRED, EXCHANGED, MORTGAGED,
PLEDGED OR OTHERWISE DISPOSED OF EXCEPT (I) PURSUANT TO AN EFFECTIVE
REGISTRATION STATEMENT UNDER THE ACT AND ANY APPLICABLE STATE SECURITIES LAWS,
OR (II) UPON RECEIPT OF AN OPINION OF THE COUNSEL TO THE TRANSFEROR, REASONABLY
ACCEPTABLE TO THE ISSUER, THAT SUCH SALE, TRANSFER, PLEDGE, HYPOTHECATION, OR
OTHER DISPOSITION IS PURSUANT TO AN AVAILABLE EXEMPTION FROM SUCH REGISTRATION.
BY ITS ACCEPTANCE HEREOF, THE HOLDER OF THIS CERTIFICATE REPRESENTS THAT IT IS
ACQUIRING SUCH SECURITIES FOR INVESTMENT PURPOSES ONLY AND NOT WITH A VIEW
TOWARD THE DISTRIBUTION OR RESALE THEREOF, AND AGREES TO COMPLY WITH THE WARRANT
AGREEMENT, DATED AS OF MARCH 12, 1999, BY AND AMONG EVERCOM, INC., A DELAWARE
CORPORATION (THE "COMPANY") AND THE HOLDER, THE REGISTRATION RIGHTS AGREEMENT
DATED AS OF DECEMBER 27, 1996 BY AND AMONG THE COMPANY, AND ITS SHAREHOLDERS AND
WARRANTHOLDERS, AND THE SHAREHOLDERS AGREEMENT DATED AS OF

                                      -2-
<PAGE>
 
DECEMBER 27, 1996 BY AND AMONG THE COMPANY, AND ITS SHAREHOLDERS AND
WARRANTHOLDERS.
 
     Any warrant or certificate issued at any time in exchange or substitution
for any warrant or certificate bearing such legend shall also bear the above
legend unless, in the opinion of the Company's counsel or such other counsel as
shall be reasonably approved by the Company, the securities represented thereby
are no longer subject to the restrictions referred to in such legend.
 
     1.6. Investment Letter.  Simultaneously with the delivery to the Holder of
          -----------------                                                    
certificates or other documents representing the Shares and/or any substitute
Warrant, the Holder will execute and deliver to the Company a letter, in the
following form of EXHIBIT 1.6 hereto, representing to the Company as follows:
                  -----------                                                
 
          (a) The Holder is acquiring the Shares and the Warrant for the
Holder's own account (and not for the account of others), for investment and not
with a view to the distribution or resale thereof;
 
          (b) The Holder is an "accredited investor", as defined in Rule 501
promulgated under the Securities Act of 1933, as amended (the "1933 Act");
 
          (c) The Holder understands that the Holder may not sell or dispose of
the Shares or the Warrant in the absence of either a registration statement
under the 1933 Act or an exemption from the registration provisions of the 1933
Act;
 
          (d) The Holder understands that the Warrant and the Shares are subject
to restrictions on transfer as provided in the Shareholders Agreement;
 
          (e) The Holder understands and agrees that if he should decide to
dispose of or transfer any of the Shares or the Warrant, he may dispose of them
only (i) to an "accredited investor", (ii) in compliance with the 1933 Act, as
then in effect, and (iii) upon delivery to the Company of an opinion, in form
and substance reasonably satisfactory to the Company, of recognized securities
counsel to the effect that the disposition or transfer is to be made in
compliance with all applicable federal and state securities laws; and
 
          (f) The Holder understands that stop-transfer instructions to the
foregoing effect will be in effect with respect to the Shares and the Warrant.
 
     2.   Exchange of Warrant Certificate.  Subject in all respects to the
          -------------------------------                                 
limitations on transferability and divisibility of Section 1 hereof, any
certificate evidencing all or a portion of the Warrant may be exchanged for
another certificate or certificates entitling the Holder to purchase a like
aggregate number of Shares as the certificate or certificates surrendered then
entitling such Holder to purchase. Any Holder desiring to exchange a certificate
evidencing all or a portion of the Warrant, shall make such request in writing
delivered to the Company, and shall surrender, properly endorsed, the
certificate evidencing the portion of the Warrant to be so exchanged. 

                                      -3-
<PAGE>
 
Thereupon, the Company shall, within five (5) business days, execute and deliver
to the person entitled thereto a new certificate evidencing all or a portion of
the Warrant as so requested.

     3.   Term of Warrants; Exercise of Warrants.
          -------------------------------------- 

          (a) Subject to the terms of this Agreement, the Holder shall have the
right, at any time during the period commencing at 9:00 a.m. New York, New York
time, on March 12, 1999 (the "Exercisability Date" ), and ending at 5:00 p.m.,
New York, New York time, on December 31, 2007 (the "Termination Date"), to
purchase from the Company up to the number of Shares which the Holder may at the
time be entitled to purchase pursuant to this Agreement and the portion of the
Warrant (or certificate therefor) then held by it, upon surrender to the
Company, at its principal office in Dallas, Texas, of the certificate evidencing
the portion of the Warrant to be exercised together with the purchase form duly
filled in and signed, and upon payment to the Company of the portion of the
Warrant Price, as defined in and determined in accordance with the provisions of
Sections 6 and 7 hereof, allocable to the number of Shares with respect to which
such portion of the Warrant is then exercised. Payment of the Warrant Price
shall be made (i) in cash, by cashier's check or by wire transfer or (ii)
through the surrender of debt, preferred equity securities or Common Stock of
the Company having a principal amount, liquidation preference, or current market
price, as the case may be, equal to the aggregate Warrant Price to be paid (to
the extent then due and payable, the Company will pay the accrued interest or
dividends on such surrendered debt, preferred equity securities, or Common Stock
in cash at the time of surrender and, if not due and payable at the time of
surrender, the Company will issue a like debt instrument or preferred equity
securities in the amount of such accrued interest or dividend, as the case may
be) or (iii) through "cashless" or "net-issue" exercise provided in Section 3(b)
below.
 
          (b) The holder of the Warrant may also exercise the Warrant in a
"cashless" or "net-issue" exercise by delivery to the Company of (a) the written
notice described in Section 3(a) above, (b) the Warrant and (c) written notice
that the holder elects to make payment of the Warrant Price, in full or in part,
by surrender of its right to purchase certain shares of Common Stock pursuant to
the Warrant. For purposes of this Section 3(b), the value of the surrender of
the right to purchase a share of Common Stock shall be attributed a value equal
to (i) the current market price per share of Common Stock minus (ii) the then
Warrant Price per share of Common Stock. If the determination of current market
price per share of Common Stock is to be made for a "cashless" or "net-issue"
exercise in connection with an initial public offering of Common Stock, the
current market price per share of Common Stock shall equal the per share
offering price without deductions for any compensation, discounts or expenses
paid or incurred by the Company in connection with such offering. Otherwise, the
current market price shall be determined in accordance with the provisions of
Section 7.1(f) hereof.
 
          (c) Upon such surrender of the Warrant (or certificate therefor) and
payment of such Warrant Price as aforesaid, or after "cashless" or "net issue"
exercise, the Company shall, within five (5) business days, issue and cause to
be delivered to or upon the written order of the Holder, and in such name or
names as the Holder may designate, certificate or certificates for the 

                                      -4-
<PAGE>
 
number of full Shares so purchased upon the exercise of the Warrant, together
with cash, as provided in Section 8 hereof, with respect to any fractional
Shares otherwise issuable upon such surrender and the cash, property and other
securities to which the Holder is entitled pursuant to the provisions of Section
7. The Warrant shall be exercisable, at the election of the Holder, either in
whole or from time to time in part and, in the event that the certificate
evidencing the Warrant is exercised with respect to less than all of the Shares
specified therein at any time prior to the Termination Date, a new certificate
evidencing the remaining Warrant shall be issued by the Company.
 
     4.   Payment of Taxes.  The Company shall pay all documentary stamp taxes,
          ----------------                                                     
if any, attributable to the initial issuance of the Shares; provided that the
Company shall not be required to pay any tax or taxes which may be payable with
respect to any secondary transfer of the Warrant or the Shares.

     5.   Mutilated or Missing Warrant.  In case the certificate or certificates
          ----------------------------                                          
evidencing the Warrant shall be mutilated, lost, stolen or destroyed, the
Company shall, at the request of the Holder, issue and deliver in exchange and
substitution for and upon cancellation of the mutilated certificate or
certificates, or in lieu of and substitution for the certificate or certificates
lost, stolen or destroyed, a new Warrant certificate or certificates of like
tenor and representing an equivalent right or interest, but only upon receipt of
evidence satisfactory to the Company of such loss, theft or destruction of such
Warrant and of a bond of indemnity, if requested, also satisfactory in form and
amount at the applicant's cost. Applicants for such substitute Warrant
certificate shall also comply with such other reasonable regulations and pay
such other reasonable charges as the Company may prescribe, not to exceed Two
Hundred Fifty and no/100 Dollars ($250) per occurrence.

     6.   Warrant Price.
          ------------- 

     6.1. Warrant Price. The per Share price (the "Warrant Price") at which
          -------------                                                    
Shares shall be purchasable upon the exercise of the Warrant is $1,000, subject
to adjustment pursuant to Section 7 hereof.
 
     7.   Adjustment of Warrant Price and Number of Shares.
          ------------------------------------------------ 

     7.1. Adjustment of Warrant Price and Number of Shares.  After the issuance
          ------------------------------------------------                     
of the Warrant, the number and kind of securities purchasable upon the exercise
of the Warrant and the Warrant Price shall be subject to adjustment from time to
time upon the happening of certain events, as follows:
 
          (a) Adjustments for Change in Capital Stock.  In the event the Company
              ---------------------------------------                           
shall (A) pay a stock dividend or make a distribution to holders of Common Stock
in shares of its Common Stock, (B) subdivide its outstanding shares of Common
Stock into a larger number of shares, (C) combine its outstanding shares of
Common Stock into a smaller number of shares, (D) make a distribution on its
Common Stock in shares of its capital stock other than Common Stock 

                                      -5-
<PAGE>
 
or preferred stock, (E) issue by reclassification of its shares of Common Stock
any shares of capital stock of the Company, or (F) take any action which would
result in any of the foregoing, then the Warrant Price and the number and kind
of shares of capital stock of the Company issuable upon exercise of a Warrant as
in effect immediately prior to such action shall then be proportionally adjusted
so that the holder of any Warrant thereafter exercised may receive the aggregate
number and kind of shares of capital stock of the Company which he would have
owned immediately following such action if such Warrant had been exercised
immediately prior to such action.
 
     An adjustment made pursuant to this Section 7.1(a)(i) shall become
effective retroactively immediately after the record date in the case of a
dividend or distribution of Common Stock and shall become effective immediately
after the effective date in the case of a subdivision, combination or
reclassification. If after an adjustment a holder of a Warrant upon exercise of
it may receive shares of two or more classes of capital stock of the Company,
the Company shall determine the allocation of the adjusted Warrant Price between
the classes of capital stock. After such allocation, the exercise privilege and
the Warrant Price of each class of capital stock shall thereafter be subject to
adjustment on terms comparable to those applicable to Common Stock in this
Section.

          (b) Adjustment for Rights Issue.  If the Company distributes any
              ---------------------------                                 
rights, options or warrants to any holder of its Common Stock entitling them for
a period expiring within 60 days after the record date mentioned below to
purchase shares of Common Stock at a price per share less than the current
market price per share on that record date, the Warrant Price shall be adjusted
in accordance with the formula:

                                    O +    N  x  P
                                       ----------------
                         W' = W x             M
                                   --------------------
                                           O  +  N
     Where:
 
          W' = the adjusted Warrant Price

          W  = the current Warrant Price

          O  = the number of shares of Common Stock outstanding on the record
               date

          N  = the number of additional shares of Common Stock offered

          P  = the offering price per share of the additional shares

          M  = the current market price per share of Common Stock on the record
               date

                                      -6-
<PAGE>
 
          The adjustment shall be made successively whenever any such rights,
options or warrants are issued and shall become effective immediately after the
record date for the determination of stockholders entitled to receive the right,
options or warrants. If at the end of the period during which such rights,
options or warrants are exercisable, not all rights, options or warrants shall
have been exercised, the Warrant Price shall be immediately readjusted to what
it would have been if "N" in the above formula had been the number of shares
actually issued.
 
          (c) Adjustment for Other Distributions.  If the Company distributes to
              ----------------------------------                                
any holder of its Common Stock any of its assets (including but not limited to
cash, debt securities, preferred stock, or any rights or warrants to purchase
debt securities, preferred stock, assets or other securities of the Company),
the Warrant Price shall be adjusted in accordance with the formula:

                              W' = W x       M - F
                                      -----------------
                                               M

     Where:

          W' = the adjusted Warrant Price

          W  = the current Warrant Price

          M  = the current market price per share of Common Stock outstanding on
the record date mentioned below

          F  = the Fair Market Value on the record date of the net assets,
securities, rights or warrants applicable to one share of Common Stock.

          The adjustment shall be made successively whenever any such
distribution is made and shall become effective immediately after the record
date for the determination of stockholders entitled to receive the distribution.

          This subsection does not apply to rights, options or warrants referred
to in subsection (b) of this Section 7.1.

          (d) Adjustment for Common Stock Issue.  If the Company issues shares
              ---------------------------------                               
of Common Stock for a consideration per share less than the current market price
per share on the date the Company fixes the offering price of such additional
shares, the Warrant Price shall be adjusted in accordance with the formula:

                                                P
                                       ------------------
                              W' = W x      O + M
                                       ------------------
                                                A

                                      -7-
<PAGE>
 
     Where:
 
          W' = the adjusted Warrant Price

          W  = the then current Warrant Price

          O  = the number of shares outstanding immediately prior to the
issuance of such additional shares

          P  = the aggregate consideration received for the issuance of such
additional shares

          M  = the current market price per share on the date of issuance of
such additional shares

          A  = the number of shares outstanding immediately after the issuance
of such additional shares

          The adjustment shall be made successively whenever any such issuance
is made, and shall become effective after such issuance.

          This subsection (d) does not apply to:

               (1) any of the transactions described in subsections (b) and (c)
     of this Section 7.1 or

               (2) Common Stock issued in a bona fide public offering pursuant
     to a firm commitment underwriting or

               (3) Shares of Common Stock issued pursuant to existing options or
     the exchange of convertible securities on the date hereof.

          (e)  Adjustment for Convertible Securities or Options Issue.  If the
               ------------------------------------------------------         
Company issues any securities convertible into or exchangeable for Common Stock
or options, rights or warrants to subscribe for, purchase or otherwise acquire
any class of Common Stock or convertible securities (other than securities
issued in transactions described in subsections (b) and (c) of this Section 7.1)
for a consideration per share of Common Stock initially deliverable upon
conversion or exchange of such securities less than the current market price per
share on the date of issuance of such securities, the Warrant Price shall be
adjusted in accordance with this formula:

                                                  P
                                        ------------------
                               W' = W x       O + M
                                        ------------------
                                              O + D

                                      -8-
<PAGE>
 
     Where: 

          W' = the adjusted Warrant Price

          W  = the then current Warrant Price

          O  = the number of shares outstanding immediately prior to the
issuance of such securities

          P  = the aggregate consideration received for the issuance of such
securities

          M  = the current market price per share on the date of issuance of
such securities or to be received upon the exercise of such securities

          D  = the maximum number of shares deliverable upon conversion,
exercise or in exchange for such securities at the initial conversion price,
exercise price or exchange rate

          The adjustment shall be made successively whenever any such issuance
is made, and shall become effective immediately after such issuance.

          No further adjustment in the Warrant Price shall be made upon the
subsequent issue of convertible securities or shares of Common Stock upon the
exercise of options or conversion or exchange of such convertible securities.

          If all of the Common Stock deliverable upon conversion or exchange of
such securities have not been issued when such securities are no longer
outstanding, then the Warrant Price shall promptly be readjusted to the Warrant
Price which would then be in effect had the adjustment upon the issuance of such
securities been made on the basis of the actual number of shares of Common Stock
issued upon conversion or exchange of such securities.

          This subsection (e) does not apply to convertible securities issued in
a bona fide public offering pursuant to a firm commitment underwriting.

          (f)  Current Market Price.
               -------------------- 
 
               (1) In Section 3(b) and subsections (b), (c), (d) and (e) of this
     Section 7.1(a) the current market price per share of Common Stock on any
     date is:
 
          (i) if the Common Stock is not registered under the Exchange Act,
     then, based upon the Fair Market Value of 100% of the Company if sold as a
     going concern and without regard to any discount for the lack of liquidity
     or on the basis that the relevant shares of the Common Stock do not
     constitute a majority or controlling interest in the Company; or

                                      -9-
<PAGE>
 
          (ii) if the Common Stock is registered under the Exchange Act, the
     average of the Quoted Prices of the Common Stock for 20 consecutive trading
     days before the date in question. The "Quoted Price" of the Common Stock is
     the last reported sales price of the Common Stock as reported by Nasdaq
     National Market, or if the Common Stock is listed on a national securities
     exchange, the last reported sales price of the Common Stock on such
     exchange (which shall be for consolidated trading if applicable to such
     exchange), or if neither so reported or listed, the last reported bid price
     of the Common Stock. In the absence of one or more such quotations, the
     current market price of the Common Stock shall be determined as if the
     Common Stock was not registered under the Exchange Act.
 
               (2) Fair Market Value.  Fair Market Value means the value
                   -----------------                                    
     obtainable upon a sale in an arm's length transaction to a third party
     under usual and normal circumstances, with neither the buyer nor the seller
     under any compulsion to act, with equity to both, as determined by the
     Board in good faith; provided, however, that if the holder of this Warrant
                          --------  -------                                    
     shall dispute the Fair Market Value as determined by the Board, such holder
     may undertake to have it and the Company retain an Independent Expert. The
     determination of Fair Market Value by the Independent Expert shall be
     final, binding and conclusive on the Company and such holder. All costs and
     expenses of the Independent Expert shall be borne by such holder unless the
     Fair Market Value as determined by the Independent Expert exceeds the Fair
     Market Value as determined by the Board by 5% but less than 10%, in which
     case the cost of the Independent Expert shall be shared equally by such
     holder and the Company, and unless the Fair Market Value as determined by
     the Independent Expert exceeds the Fair Market Value as determined by the
     Board by 10% or more, in which case the cost of the Independent Expert
     shall be borne solely by the Company.
 
               (3) Independent Expert.  Independent Expert means an investment
                   ------------------                                         
     banking firm reasonably agreeable to the Company and the holder of this
     Warrant who does not (and whose affiliates do not) have a financial
     interest in the Company or any of its affiliates.
 
          (g)  Consideration Received.  For purposes of any computation
               ----------------------                                  
respecting consideration received pursuant to subsections (d) and (e) of this
Section 7.1, the following shall apply:
 
               (1) in the case of the issuance of shares of Common Stock for
     cash, the consideration shall be the amount of such cash, provided that in
     no case shall any deduction be made for any commissions, discounts or other
     expenses incurred by the Company for any underwriting of the issue or
     otherwise in connection therewith;
 
               (2) in the case of the issuance of shares of Common Stock for a
     consideration in whole or in part other than cash, the consideration other
     than cash shall be deemed to be the Fair Market Value thereof;
 

                                      -10-
<PAGE>
 
               (3) in the case of the issuance of securities convertible into or
     exchangeable for shares, the aggregate consideration received therefor
     shall be deemed to be the consideration received by the Company for the
     issuance of such securities plus the additional minimum consideration, if
     any, to be received by the Company upon the conversion or exchange thereof
     (the consideration in each case to be determined in the same manner as
     provided in clauses (1) and (2) of this subsection).
 
          (h)  When De Minimis Adjustment May Be Deferred.  No adjustment in the
               ------------------------------------------                       
Warrant Price need be made unless the adjustment would require an increase or
decrease of at least 1% in the Warrant Price. Any adjustments that are not made
shall be carried forward and taken into account in any subsequent adjustment.
 
          All calculations under this Section shall be made to the nearest cent
or to the nearest 1/100th of a share, as the case may be.
 
          (i) Notice of Adjustment.  Whenever the Warrant Price is adjusted, the
              --------------------                                              
Company shall provide the notice required by Section 11 hereof.
 
          (j) Voluntary Reduction.  The Company from time to time may reduce the
              -------------------                                               
Warrant Price by any amount for any period of time if the period is at least 20
days and if the reduction is irrevocable during the period; provided, however,
                                                            --------  ------- 
that in no event may the Warrant Price be less than the par value of a share of
Common Stock.
 
          Whenever the Warrant Price is reduced, the Company shall mail to
Warrant holders a notice of the reduction. The Company shall mail the notice at
least 15 days before the date the reduced Warrant Price takes effect. The notice
shall state the reduced Warrant Price and the period it will be effect.
 
          A reduction of the Warrant Price does not change or adjust the Warrant
Price otherwise in effect for purposes of subsections (a), (b), (c), (d) and (e)
of this Section 7.1.
 
          (k) Adjustment in Number of Shares.  Upon each adjustment of the
              ------------------------------                              
Warrant Price pursuant to this Section 7.1, each Warrant outstanding prior to
the making of the adjustment in the Warrant Price shall thereafter evidence the
right to receive upon payment of the adjusted Warrant Price that number of
shares of Common Stock (calculated to the nearest hundredth) obtained from the
following formula:

                              N' = N   x  W
                                         ---
                                          W'
                                                                               
     Where:

          N' = the adjusted number of Warrant Shares issuable upon exercise of a
Warrant by payment of the adjusted Warrant Price

                                      -11-
<PAGE>
 
          N  = the number of Warrant Shares previously issuable upon exercise of
a Warrant by payment of the Warrant Price prior to adjustment

          W' = the adjusted Warrant Price

          W  = the Warrant Price prior to adjustment.

          (l) In calculating any adjustment hereunder, the Warrant Price shall
be calculated to the nearest cent and the number of Shares purchasable hereunder
shall be calculated to the nearest .001 of a share.
 
          (m) In the event that at any time, as a result of an adjustment made
pursuant to this Section 7, the Holder shall become entitled to purchase any
securities of the Company other than Class A Common Stock, the Company shall
duly reserve such securities for issuance and thereafter the number of such
other securities so purchasable upon exercise of the Warrant and the Warrant
Price of such securities shall be subject to the adjustment from time to time in
a manner and on terms as nearly equivalent as practicable to the provisions with
respect to the Shares contained in this Section 7.
 
          (n) In any case in which the provisions of this Section 7.1 require
that the adjustment shall be effective immediately after a record date for an
event, the Company may defer until the occurrence of such event (1) issuing to
the holder of the Warrant or portion thereof exercised after such record date
and before the occurrence of such event the additional shares of Common Stock
issuable upon such exercise by reason of the adjustment required by such event
over and above the shares of Common Stock issuable upon such exercise before
giving effect to such adjustment, and (2) paying to such holder any cash in lieu
of a fractional share of Common Stock pursuant to Section 8 hereof; provided,
however, that the Company shall deliver to the holder a due bill or other
appropriate instrument evidencing such holder's right to receive additional
shares, other capital stock and cash upon the occurrence of the event requiring
such adjustment.
 
     7.2. Statement on Warrants. Irrespective of any adjustment in the Warrant
          ---------------------                                               
Price or the number or kind of Shares purchasable upon the exercise of the
Warrant, the Warrant certificate or certificates theretofore issued may continue
to express the same price and number and kind of shares as are stated in the
Warrant initially issuable pursuant to this Agreement.
 
     7.3. Reservation. The Company shall at all times reserve and keep
          -----------                                                 
available, free from preemptive rights, so long as the Warrant remains
outstanding, out of its authorized but unissued Common Stock the full number of
shares of Common Stock deliverable upon the exercise of the Warrant and shall
take all such action and obtain all such permits or orders as may be necessary
to enable the Company lawfully to issue such Common Stock.

                                      -12-
<PAGE>
 
     The Company or, if appointed, the transfer agent for the Common Stock (the
"Transfer Agent") and every subsequent transfer agent for any shares of the
Company's capital stock issuable upon the exercise of any of the rights of
purchase aforesaid will be irrevocably authorized and directed at all times to
reserve such number of authorized shares as shall be required for such purpose.
The Company will keep a copy of this Agreement on file with the Transfer Agent
and with every subsequent transfer agent for any shares of the Company's capital
stock issuable upon the exercise of the rights of purchase represented by the
Warrants. The Company will furnish such Transfer Agent a copy of all notices of
adjustments and certificates related thereto, transmitted to each holder
pursuant to Section 11 hereof.
 
     Before taking any action which would cause an adjustment pursuant to
Section 7.1 hereof to reduce the Warrant Price below the then par value (if any)
of the Shares, the Company will take any corporate action which may, in the
opinion of its counsel (which may be counsel employed by the Company), be
necessary in order that the Company may validly and legally issue fully paid and
nonassessable Shares at the Warrant Price as so adjusted.
 
     The Company covenants that all Shares which may be issued upon exercise of
Warrants will, upon issue, be fully paid, nonassessable, free of preemptive
rights and free from all taxes, liens, charges and security interests with
respect to the issue thereof.
 
     7.4. Change in Control; Merger; Reorganization.  Notwithstanding anything
          -----------------------------------------                           
to the contrary contained herein, in the event of (i) a Change of Control (as
hereinafter defined), (ii) any acquisition of the Corporation by means of merger
or other form of corporate reorganization in which outstanding shares of the
Corporation are exchanged for securities or other consideration issued, or
caused to be issued, by the acquiring corporation or its subsidiary (other than
a mere reincorporation transaction), or (iii) the sale or transfer of all or
substantially all of the assets of the Company to another person, (each, a
"Major Event"), the Company shall provide written notice of such occurrence to
the Holder (the "Change of Control Notice") at least ten (10) business days
prior to the occurrence of such Major Event. The Holder may, within ten (10)
business days of receipt of a Change of Control Notice (the "Notice Cutoff
Date"), exercise the Warrant and purchase, in accordance with the procedures set
forth in Section 3 hereof, up to such number of Shares as the Holder may be
entitled to purchase hereunder, provided however, the Holder (i) may condition
the exercise of the Warrant and the purchase of the Shares upon consummation of
the Major Event, (ii) may require that the acquisition of the Shares and tender
of the Warrant Price occur contemporaneously with the consummation of the Major
Event, and (iii) may offset and/or credit against the Warrant Price any
consideration to be received by the Holder as part of the consummation of the
Major Event.
 
     For purposes of this Agreement, Change of Control shall mean the
acquisition by any person or group (as such term is defined in Section 13(d)(3)
of the Securities Exchange Act of 1934, as amended, (the "1934 Act") of
beneficial ownership (as such term is defined in Rule 13d-3 promulgated under
the 1934 Act) of more than 25% of the outstanding shares of Common Stock of the
Company.
 

                                      -13-
<PAGE>
 
     8.   Obtaining Stock Exchange Listings.  The Company will from time to time
          ---------------------------------                                     
take all action which may be necessary so that the Shares, immediately upon
their issuance upon the exercise of Warrants, will be listed on the principal
securities exchanges and markets within the United States of America, if any, on
which other shares of Common Stock are then listed.

     9.   Fractional Interests.  The Company shall be required to issue
          --------------------                                         
fractional Shares on the exercise of the Warrant.

     10.  No Rights as Stockholder.  Nothing contained in this Agreement or in
          ------------------------                                            
the Warrant shall be construed as conferring upon the Holder or its transferee
any rights as a stockholder of the Company.

     11.  Notices.  Any notice pursuant to this Agreement by the Company or by
          -------                                                             
the Holder shall be in writing and shall be deemed to have been duly given if
delivered personally with written receipt acknowledged or mailed by certified
mail five days after mailing, return receipt requested:

          If to the Holder:

          SHAREHOLDER
          COMPANY
          ADDRESS
          CITY, STATE ZIP
          CONFIDENTIAL


          If to the Company:

          8201 Tristar Drive
          Irving, Texas  75063
          Attention:  Chief Executive Officer

     Each party hereto may from time to time change the address to which notices
to it are to be delivered or mailed hereunder by notice in accordance herewith
to the other party.

     Upon any adjustment of the Warrant Price pursuant to Section 7.1, the
Company shall promptly thereafter (i) cause to be filed with the Company a
certificate of a firm of independent public accountants of recognized standing
selected by the Board of Directors of the Company (who may be the regular
auditors of the Company) setting forth the Warrant Price after such adjustment
and setting forth in reasonable detail the method of calculation and the facts
upon which such calculations are based and setting forth the number of Shares
(or portion thereof) issuable after such adjustment in the Warrant Price, upon
exercise of a Warrant and payment of the adjusted Warrant Price, which
certificate shall be conclusive evidence of the correctness of the matters set
forth therein, and (ii) cause to be given to each of the registered holders of
the Warrants at his address appearing on the Warrant register written notice of
such adjustments by first class mail, postage prepaid. Where appropriate, such
notice may be given in advance and 

                                      -14-
<PAGE>
 
included as a part of the notice required to be mailed under the other
provisions of this Section 11.

     In case:  (a) the Company shall authorize the issuance to all holders of
shares of Common Stock of rights, options or warrants to subscribe for or
purchase shares of Common Stock or of any other subscription rights or warrants;
(b) the Company shall authorize the distribution to all holders of shares of
Common Stock of evidences of its indebtedness or assets (other than cash
dividends or cash distributions payable out of consolidated earnings or earned
surplus or dividends payable in shares of Common Stock or distributions referred
to in subsection (1) of Section 7.1 hereof); (c) of the voluntary or involuntary
dissolution, liquidation or winding up of the Company; or (d) the Company
proposes to take any action (other than actions of the character described in
Section 7.1(a)) which would require an adjustment of the Warrant Price pursuant
to Section 7; then the Company shall cause to be given to each of the registered
holders of the Warrants at his address appearing on the Warrant register, at
least 20 days prior to the applicable record date hereinafter specified, or
promptly in the case of events for which there is no record date, by first-class
mail, postage prepaid, a written notice stating (i) the date as of which the
holders of record of shares of Common Stock to be entitled to receive any such
rights, options, warrants or distribution are to be determined, or (ii) the
initial expiration date set forth in any tender offer or exchange offer for
shares of Common Stock. The failure to give the notice required by this Section
11 or any defect therein shall not affect the legality or validity of any
distribution, right, option, warrant, conveyance, transfer, dissolution,
liquidation or winding up, or the vote upon any action.

     12.  Successors.  All the covenants and provisions of this Agreement by or
          ----------                                                           
for the benefit of the Company or the Holder shall bind and inure to the benefit
of their respective successors, heirs and permitted assigns.

     13.  Benefits of this Agreement.  Except as otherwise provided herein,
          --------------------------                                       
nothing in this Agreement shall be construed to give to any person or
corporation other than the Company and the Holder any legal or equitable right,
remedy or claim under this Agreement, and this Agreement shall be for the sole
and exclusive benefit of the Company and the Holder.

     14.  Further Assurances.  The Company hereby agrees promptly to execute, at
          ------------------                                                    
the Holder's reasonable request after the issuance of the Warrant, any documents
or materials related to the transactions contemplated by this Agreement.

     15.  Time of Essence.  Time is of the essence in interpreting and
          ---------------                                             
performing this Agreement.

     16.  Severability.  In case any provision in this Agreement shall be held
          ------------                                                        
invalid, illegal or unenforceable, the validity, legality and enforceability of
the remaining provisions hereof will not in any way be affected or impaired
hereby.

                                      -15-
<PAGE>
 
     17.   Jury Trial; Jurisdiction.  The parties waive the right to a jury
           ------------------------     
trial with respect to any controversy or claim between or among the parties
hereto, including but not limited to those arising out of or relating to this
Agreement, including any claim based on or arising from an alleged tort.

     18.   Governing Law.  This Agreement shall be governed by and interpreted
           -------------
in accordance with the laws of the State of Delaware. The parties, in
acknowledgment that they have been represented by counsel and that this
Agreement has been carefully negotiated, agree that the construction and
interpretation of this Agreement and other documents entered into in connection
herewith shall not be affected by the identity of the party under whose
direction or at whose expense this Agreement and such documents were prepared or
drafted.

     19.   Attorneys' Fees.  In the event of any disputes arising hereunder
           ---------------                                                 
concerning the interpretation or enforcement of this Agreement, a party shall be
entitled to recover from the party determined to be in breach its attorneys'
fees, costs and expenses.

     20.   Specific Performance.  Each of the parties shall be entitled to
           --------------------                                           
specific performance in the event of a breach by the other party of their
respective obligations hereunder. Such remedy shall be in addition to, but shall
not replace, any other remedies which might be available under this Agreement,
at law or in equity, including without limitation, actions for attorney's fees.

     21.   Registration Rights.  The Shares issuable upon exercise of this
           -------------------                                            
Warrant are subject to certain rights and restrictions pursuant to the
Registration Rights Agreement and the Shareholders Agreement.

     22.   Representations of Company.  The Company represents and warrants to
           --------------------------                                         
Holder as follows:

     22.1. Corporate Organization and Good Standing.  The Company is a
           ----------------------------------------                   
corporation duly organized, validly existing, and in good standing under the
laws of the State of Delaware and is duly qualified and in good standing in all
other states where the nature of its business or operations or the ownership of
its property requires such qualification.
 
     22.2. Corporate Approval.  The Company has full corporate power and
           ------------------                                           
authority to execute and deliver this Agreement and all other documents and
agreements to be executed and delivered by it hereunder ("Transaction
Documents") and to consummate the transactions contemplated hereby. The board of
directors of the Company has duly and validly approved the execution, delivery,
and performance of this Agreement and the transactions contemplated herein. No
other corporate or legal proceedings on the part of the Company are necessary to
approve and authorize the execution and delivery of this Agreement and the
consummation of the transactions contemplated hereby. This Agreement
constitutes, and the other Transaction Documents, when executed, will
constitute, the legal, valid, and binding obligation and agreement of the
Company enforceable against the Company in accordance with its terms, subject
only to the general law of creditors' rights.
 

                                      -16-
<PAGE>
 
     23.  Certain Terms.  As used herein, the following terms shall have the
          -------------                                                     
meanings set forth below:

          "Common Stock" shall mean (A) the class of stock designated as the
           ------------                                                     
Class A Common Stock and Class B Common Stock of the Company at the date of this
Agreement, or (B) any other class of stock resulting from successive changes or
reclassifications of such Common Stock.

          "Common Stock Equivalents" shall mean (without duplication with any
           ------------------------                                          
other Common Stock or Common Stock Equivalents) rights, warrants, options,
convertible securities or indebtedness, exchangeable securities or indebtedness,
or other rights, exercisable for or convertible or exchangeable into, directly
or indirectly, Common Stock and securities convertible or exchangeable into
Common Stock, whether at the time of issuance, upon the passage of time, or upon
the occurrence of some future event.



                     [SEE FOLLOWING PAGES FOR SIGNATURES]

                                      -17-
<PAGE>
 
Corporation or Trust:                        Address:
                                             -------

____________________________________         ___________________________________
                                             ___________________________________
____________________________________         ___________________________________
(name of entity)       
 
By:_________________________________          __________________________________
Print Name:______________________                     Tax Payer Id. No.
Title:___________________________    
 
 
Partnership:                                 Address:
                                             -------
 
____________________________________         ___________________________________
(name of partnership)                        ___________________________________
                                             ___________________________________

By:_________________________________         ___________________________________
      (name of general partner)                       Tax Payer Id. No.


By:_________________________________ 
Print Name:______________________    
Title:___________________________    
 
 
 
Individual(s):                               Address:
                                             -------
(indicate style of ownership if more          
than one (1) individual (e.g. JTWROS)        ___________________________________
                                             ___________________________________
____________________________________         ___________________________________

Print Name:______________________            ___________________________________
                                                      Social Security No.

____________________________________         ___________________________________
Print Name:______________________                     Social Security No.
Style of Ownership:______________                                          
                                                      

                         SIGNATURE PAGE FOR THE HOLDER
<PAGE>
 
"Company"                                    EVERCOM, INC.,
                                             a Delaware corporation
 
 
 
                                             By:    /s/ JEFFREY D. CUSHMAN
                                                    ----------------------------
                                             Name:  Jeffrey D. Cushman
                                             Title: Vice President
<PAGE>
 
EXHIBIT 1.4A to
------------   
Warrant Agreement


WARRANT NO.___________


     "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
     UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"). SUCH
     SECURITIES MAY NOT BE SOLD, ASSIGNED, TRANSFERRED, EXCHANGED, MORTGAGED,
     PLEDGED OR OTHERWISE DISPOSED OF EXCEPT (I) PURSUANT TO AN EFFECTIVE
     REGISTRATION STATEMENT UNDER THE ACT AND ANY APPLICABLE STATE SECURITIES
     LAWS, OR (II) UPON RECEIPT OF AN OPINION OF THE COUNSEL TO THE TRANSFEROR,
     REASONABLY ACCEPTABLE TO THE ISSUER, THAT SUCH SALE, TRANSFER, PLEDGE,
     HYPOTHECATION, OR OTHER DISPOSITION IS PURSUANT TO AN AVAILABLE EXEMPTION
     FROM SUCH REGISTRATION. BY ITS ACCEPTANCE HEREOF, THE HOLDER OF THIS
     CERTIFICATE REPRESENTS THAT IT IS ACQUIRING SUCH SECURITIES FOR INVESTMENT
     PURPOSES ONLY AND NOT WITH A VIEW TOWARD THE DISTRIBUTION OR RESALE
     THEREOF, AND AGREES TO COMPLY WITH THE WARRANT AGREEMENT, DATED AS OF MARCH
     12, 1999, BY AND AMONG EVERCOM, INC., A DELAWARE CORPORATION (THE
     "COMPANY") AND ____________________________ (THE "HOLDER"), THE
     REGISTRATION RIGHTS AGREEMENT DATED AS OF DECEMBER 27, 1996 BY AND AMONG
     THE COMPANY, AND ITS SHAREHOLDERS AND WARRANTHOLDERS, AND THE SHAREHOLDERS
     AGREEMENT DATED AS OF DECEMBER 27, 1996 BY AND AMONG THE COMPANY, AND ITS
     SHAREHOLDERS AND WARRANTHOLDERS."



                          WARRANT TO PURCHASE SHARES
                          OF CLASS A COMMON STOCK OF
                         EVERCOM, INC. $.01 PAR VALUE

                    Exercisable commencing March 12, 1999;
                         Void after December 31, 2007;


     THIS CERTIFIES that, for value received, _______________________________
____________________________________________________ ("Holder"), or registered
assigns, is entitled, subject to the terms and conditions set forth in this
Warrant, to purchase from Evercom, Inc., a Delaware corporation (the "Company"),
up to ___________ shares of Class A Common Stock, $0.01 par value ("Shares"), of
the Company commencing at 9:00 a.m., Eastern 

                          Exhibit 1.4A - Page 1 of 3
<PAGE>
 
time, on March 12, 1999, and continuing up to 5 p.m. Eastern time on December
31, 2007, at an initial per share price of $1,000.00. This Warrant is issued
pursuant to a Warrant Agreement between the Holder and the Company dated as of
March 12, 1999, the terms of which are incorporated by reference herein and made
a part of this instrument and are referred to for a description of the rights,
limitation of rights, obligations, duties and immunities thereunder of the
Company and the holders of the Warrant. This Warrant is also subject to the
terms and obligations of the Shareholders Agreement dated December 27, 1996 by
and among the Company, the Holder and the other warrantholders and shareholders
of the Company.

     This Warrant may be exercised by the holder hereof, in whole or in part by
the presentation and surrender of this Warrant with the form of Election to
Purchase duly executed, at the principal office of the Company (or at such other
address as the Company may designate by notice in writing to the holder hereof
at the address of such holder appearing on the books of the Company), and upon
payment to the Company of the purchase price in cash, by cashier's check, or by
wire transfer or partially in cash, cashier's check or wire transfer and the
remainder pursuant to Section 3 of the Warrant Agreement. Certificates for the
Shares so purchased shall be delivered or mailed to the Holder promptly after
this Warrant shall have been so exercised, and, unless this Warrant has expired
or has been exercised in full, a new Warrant identical in form but representing
the number of Shares with respect to which this Warrant shall not have been
exercised shall also be issued to the holder hereof.

     The Warrant Agreement provides that upon the occurrence of certain events
the Warrant Price set forth on the face hereof may, subject to certain
conditions, be adjusted. If the Warrant Price is adjusted, the Warrant Agreement
provides that the number of shares of Common Stock issuable upon the exercise of
each Warrant shall be adjusted. Fractions of a share of Common Stock may be
issued upon the exercise of any Warrant.

     Nothing contained herein shall be construed to confer upon the holder of
this Warrant, as such, any of the rights of a shareholder of the Company.

                          Exhibit 1.4A - Page 2 of 3
<PAGE>
 
Dated:  March 12, 1999             EVERCOM, INC.,
                                   a Delaware corporation



                                   By:  ________________________________

                          Exhibit 1.4A - Page 3 of 3
 
<PAGE>
 
EXHIBIT 1.4B to
------------   
Warrant Agreement



                          ___________________________



                             ELECTION TO PURCHASE
                             --------------------



___________________:

     The undersigned hereby irrevocably elects to exercise the right of purchase
represented by the within Warrant for, and to purchase thereunder, _________
Shares provided for therein, and requests that certificates for the Shares be
issued in the name of:



     (Please Print Name, Address and Tax Identification Number) and, if said
number of Shares shall not be the total number of Shares purchasable hereunder,
that a new Warrant certificate for the balance of the Shares purchasable under
the within Warrant certificate be registered in the name of the undersigned
Holder or its assignee as below indicated and delivered to the address stated
below:

Dated: ________________, _________


          Name of Holder or Assignee (Please Print):

          _____________________________________

          Address: _________________________________________
 
          Signature:________________________________________


     Signature Guaranteed: Note: The above signature must correspond with the
name as written upon the face of this Warrant certificate in every particular,
without alteration or enlargement or any change whatever, unless this Warrant
has been assigned.

                 (To be signed only upon assignment of Warrant)

                          Exhibit 1.4B - Page 1 of 2
<PAGE>
 
     FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers
unto

__________________________________
__________________________________
__________________________________
__________________________________
__________________________________


(Name and Address of Assignee must be Printed or Typewritten) the within
Warrant, hereby irrevocably constituting and appointing ___________________
Attorney to transfer said Warrant on the books of the Company, with full power
of substitution in the premises.

Dated: _________________, __________



                                         ____________________________________
                                         Signature of Registered Holder


            Signature Guaranteed: Note:  The above signature of this assignment
                                         must correspond with the name as
                                         written upon the face of the within
                                         Warrant certificate in every
                                         particular, without alteration or
                                         enlargement or any change whatever.

                          Exhibit 1.4B - Page 2 of 2
<PAGE>
 
EXHIBIT 1.6 to
-----------   
Warrant Agreement



                            [letterhead of Holder]



____________________, 19 _____


EVERCOM, INC.:


     The undersigned warrantholder ("Holder") hereby represents and warrants to
you as follows:


          (a) The Holder is acquiring the Shares and the Warrant for Holder's
     own account (and not for the account of others), for investment and not
     with a view to the distribution or resale thereof;

          (b) The Holder is an "accredited investor", as defined in Rule 501
     promulgated under the Securities act of 1933, as amended (the "1933 Act");

          (c) The Holder understands that Holder may not sell or dispose of the
     Shares or the Warrant in the absence of either a registration statement
     under the 1933 Act or an exemption from the registration provisions of the
     1933 Act;

          (d) The Holder understands that the Warrant and the Shares are subject
     to restrictions on transfer as provided in the Shareholders Agreement;

          (e) The Holder understands and agrees that if he should decide to
     dispose of or transfer any of the Shares or the Warrant, he may dispose of
     them only (i) to an "accredited investor", (ii) in compliance with the 1933
     Act, as then in effect, and (iii) upon delivery to the Company of an
     opinion, in form and substance reasonably satisfactory to the Company, of
     recognized securities counsel to the effect that the disposition or
     transfer is to be made in compliance with all applicable federal and state
     securities laws; and

          (f) The Holder understands that stop-transfer instructions to the
     foregoing effect will be in effect with respect to the Shares and the
     Warrant.

                           Exhibit 1.6 - Page 1 of 2
<PAGE>
 
     IN WITNESS WHEREOF, the undersigned has caused this letter to be duly
executed, all as of the day and year first above written.


[HOLDER]



By: ________________________________

Title: ___________________________


                           Exhibit 1.6 - Page 2 of 2